Technical Appendix to The Economics of Density:Evidence from the Berlin Wall

Gabriel M. AhlfeldtLondon School of Economics and CEPR

Stephen J. ReddingPrinceton University, NBER and CEPR

Daniel M. SturmLondon School of Economics and CEPR

Nikolaus WolfHumboldt University and CEPR

March 11, 2015

Contents

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2A.2 Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

A.2.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4A.2.2 Distribution of Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5A.2.3 Residence and Workplace Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6A.2.4 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9A.2.5 Land Market Clearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10A.2.6 Properties of General Equilibrium with Exogenous Location

Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12A.2.7 Properties of General Equilibrium with Agglomeration Forces . . . . . . . . . . . . 18

A.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21A.3.1 Determining A, B, ϕ from α, β, µ, ε, κ and the Observed Data . . . . . . . . . 22

A.3.1.1 Wages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23A.3.1.2 Adjusted Residential Amenities . . . . . . . . . . . . . . . . . . . . . . . 25A.3.1.3 Final Goods Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 26A.3.1.4 Land Market Clearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27A.3.1.5 Utility, Amenities and Productivity . . . . . . . . . . . . . . . . . . . . . 28A.3.1.6 One-to-One Mapping from α, β, µ, ε, κ and the Observed Data to A,

B, ϕ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29A.3.2 Determining a, b from α, β, µ, ε, κ, λ, δ, η, ρ and the Observed Data . . . . . . 30

A.4 Gravity, Productivity and Amenities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1

A.4.1 Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32A.5 Structural Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

A.5.1 Structural Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35A.5.2 Moment Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37A.5.3 GMM Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A.5.4 Estimation Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39A.5.5 Identication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

A.6 Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45A.7 Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49A.8 Introducing Non-traded Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

A.8.1 Non-Traded Goods by Workplace . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51A.8.2 Non-Traded Goods by Residence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

A.9 Additional Reduced-Form Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 53A.9.1 Maps of Changes in Floor Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53A.9.2 Baseline Dierence-in-Dierence Specication . . . . . . . . . . . . . . . . . . . . 54A.9.3 Further Reduced-Form Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

A.10 Additional Structural Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55A.10.1 Gravity, Productivity and Amenities . . . . . . . . . . . . . . . . . . . . . . . . . . 55A.10.2 Structural Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

A.11 Data Sources and Denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57A.11.1 Employment at Place of Residence 1930s . . . . . . . . . . . . . . . . . . . . . . . . 57A.11.2 Employment at workplace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57A.11.3 Travel Times Between Blocks in Berlin . . . . . . . . . . . . . . . . . . . . . . . . . 59A.11.4 Block Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60A.11.5 Commuting Survey Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62A.11.6 Micro Data on Land Transactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A.1 Introduction

This technical appendix contains additional supplementary material for the paper. Section A.2 presentsa more detailed analysis of the theoretical model. We report the technical derivations of the expressionsreported in the paper. We also establish a number of results about the properties of the general equilibriumwith exogenous location characteristics and endogenous agglomeration forces.

Section A.3 calibrates the model for known parameter values and shows that there is a one-to-one map-ping from these known parameters and the observed data to unobserved location characteristics. Thereforethese unobserved location characteristics correspond to structural residuals that are functions of the pa-rameters and the observed data.

Section A.5 turns to the structural estimation of the model, where both the parameters and unobservedlocation characteristics are unknown and to be estimated. We derive the moment conditions used in the

2

estimation and review the Generalized Method of Moments (GMM) estimator as applied to our setting. Wediscuss the computational algorithms used to estimate the model and report the results of a grid search overthe parameter space that we use to characterize the properties of the GMM objective function.

Section A.6 uses the model to undertake counterfactuals for the eects of division and reunication.Section A.7 reports the results of a Monte Carlo exercise, in which we show that our estimation procedurecorrectly recovers the model parameters when the data are generated according to the model.

Section A.8 discusses an extension of the theoretical model to incorporate non-traded goods. Section A.9presents additional reduced-form empirical results discussed in the paper. Section A.10 reports additionalstructural estimation results discussed in the paper. Section A.11 contains further information about thedata sources and denitions.

A.2 Theoretical Model

In this section, we develop in further detail the theoretical model outlined in the paper. We present thecomplete technical derivations for all the expressions and results reported in the paper. In the interests ofclarity and to ensure that this section of the web appendix is self-contained, we reproduce some materialfrom the paper, but also include the intermediate steps for the derivation of expressions.

We consider a city embedded within a wider economy. The city consists of a set of discrete locations orblocks, which are indexed by i = 1, ..., S. The city is populated by an endogenous measure of H workers,who are perfectly mobile within the city and the larger economy. Each block has an eective supply of oorspace Li. Floor space can be used commercially or residentially, and we denote the endogenous fractionsof oor space allocated to commercial and residential use by θi and (1− θi), respectively.

Workers decide whether or not to move to the city before observing idiosyncratic utility shocks for eachpossible pair of residence and employment locations within the city. If a worker decides to move to the city,they observe these realizations for idiosyncratic utility, and pick the pair of residence and employmentlocations within the city that maximizes their utility. Population mobility between the city and the widereconomy implies that the expected utility from moving to the city equals the reservation level of utility inthe wider economy U . Firms produce a single nal good, which is costlessly traded within the city andlarger economy, and is chosen as the numeraire (p = 1). 1

Locations dier in terms of their nal goods productivity (Ai), residential amenities (Bi), supply of oorspace (Li) and access to the transport network (τij). We rst develop the model with exogenous values ofthese location characteristics, before endogenizing them below.

1We follow the canonical urban model in assuming a single tradable nal good and examine the ability of this canonical modelto account quantitatively for the observed impact of division and reunication. In Section A.8 of this web appendix, we discussan extension of the model to introduce a non-traded good.

3

A.2.1 Preferences

Workers are risk neutral such that the utility of worker o residing in block i and working in block j is linearin an aggregate consumption index (Cijo):2

Uijo = Cijo.

This aggregate consumption index depends on consumption of the single nal good (cijo), consumptionof residential oor space (`ijo), and three other components. First, residential amenities (Bi) that capturecommon characteristics that make a block a more or less attractive place to live (e.g. leafy streets and scenicviews). Second, the disutility from commuting from residence block i to workplace block j (dij ≥ 1). Third,there is an idiosyncratic shock that is specic to individual workers and varies with the worker’s blocksof employment and residence (zijo). This idiosyncratic shock captures the idea that individual workers canhave idiosyncratic reasons for living and working in dierent parts of the city. In particular, the aggregateconsumption index is assumed to take the Cobb-Douglas form:3

Cijo =Bizijodij

(cijoβ

)β (`ijo

1− β

)1−β

, 0 < β < 1, (1)

where the iceberg commuting cost dij = eκτij ∈ [1,∞) increases with the travel time between blocksi and j (τij). Travel time is measured in minutes and is computed based on the transport network, asdiscussed further in the data section of this web appendix (Section A.11). The parameter κ controls the sizeof commuting costs.

Although we model commuting costs in terms of utility, there is an isomorphic formulation in terms ofa reduction in eective units of labor, because the iceberg commuting cost dij = eκτij enters the indirectutility function (5) below multiplicatively. As a result, commuting costs are proportional to wages, andthis specication captures changes over time in the opportunity cost of travel time. Similarly, although wemodel the heterogeneity in commuting decisions in terms of an idiosyncratic shock to preferences, there isan isomorphic interpretation in terms of a shock to eective units of labor, because this shock zijo entersindirect utility (5) multiplicatively with the wage.

We model the heterogeneity in the utility that workers derive from living and working in dierent partsof the city following McFadden (1974) and Eaton and Kortum (2002). For each worker o living in block i andcommuting to block j, the idiosyncratic component of utility (zijo) is drawn from an independent Fréchetdistribution:

F (zijo) = e−TiEjz−εijo , Ti, Ej > 0, ε > 1, (2)

where the scale parameter Ti > 0 determines the average utility derived from living in block i, the scaleparameterEj > 0 determines the average utility derived from working in block j; and the shape parameterε > 1 controls the dispersion of idiosyncratic utility.

2To simplify the exposition, throughout the appendix, we index a worker’s block of residence by i or r and her block ofemployment by j or s unless otherwise indicated.

3For empirical evidence using US data in support of the constant housing expenditure share implied by the Cobb-Douglasfunctional form, see Davis and Ortalo-Magné (2011). The role played by residential amenities in inuencing utility is emphasizedin the literature following Roback (1982). See Albouy (2008) for a recent prominent contribution.

4

After observing her realizations for idiosyncratic utility for each pair of residence and employmentlocations, each worker chooses her blocks of residence and employment to maximize her utility, takingas given residential amenities, goods prices, factor prices, and the location decisions of other workers andrms. Each worker is endowed with one unit of labor that is supplied inelastically with zero disutility.Combining our choice of the nal good as numeraire (pi = p = 1 for all i) with the rst-order conditionsfor consumer equilibrium, we obtain the following demands for the nal good and residential land forworker o residing in block i and working in block j:

cijo = βwj, (3)

`ijo = (1− β)wjQi

, (4)

where wj is the wage received by the worker at her block of employment j (recall that commuting costsare incurred in terms of utility); Qi is the price of residential land at her block of residence i. We make thestandard assumption that income from land is accrued by absentee landlords and not spent within the city,although it is also possible to consider the case where it is redistributed lump sum to workers. Substitutingequilibrium consumption of the nal good (3) and residential land use (4) into utility (1), we obtain thefollowing expression for the indirect utility function:

U =BizijowjQ

β−1i

dij, (5)

from which the isomorphic formulation of commuting costs in terms of a reduction in eective units oflabor is apparent.

A.2.2 Distribution of Utility

Using the monotonic relationship between the aggregate consumption index (1) and the idiosyncratic com-ponent of utility, the distribution of utility for a worker living a block i and working at block j is also Fréchetdistributed:

Gij(u) = Pr[U ≤ u] = F

(udijQ

1−βi

Biwj

),

Gij(u) = e−Φiju−ε, Φij = TiEj

(dijQ

1−βi

)−ε(Biwj)

ε . (6)

From all possible pairs of blocks of residence and employment, each worker chooses the bilateral commutethat oers the maximum utility. Since the maximum of a sequence of Fréchet distributed random variablesis itself Fréchet distributed, the distribution of utility across all possible pairs of blocks of residence andemployment is:

1−G(u) = 1−S∏r=1

S∏s=1

e−Φrsu−ε ,

where the left-hand side is the probability that a worker has a utility greater than u, and the right-handside is one minus the probability that the worker has a utility less than u for all possible pairs of blocks of

5

residence and employment. Therefore we have:

G(u) = e−Φu−ε , Φ =S∑r=1

S∑s=1

Φrs. (7)

Given this Fréchet distribution for utility, the expected utility from moving to the city is:

E [u] =

∫ ∞0

εΦu−εe−Φu−εdu. (8)

Now dene the following change of variables:

y = Φu−ε, dy = −εΦu−(ε+1)du. (9)

Using this change of variables, the expected utility from moving to the city can be written as:

E [u] =

∫ ∞0

Φ1/εy−1/εe−ydy, (10)

which can be in turn written as:

E [u] = γΦ1/ε, γ = Γ

(ε− 1

ε

), (11)

where Γ(·) is the Gamma function; E is the expectations operator and the expectation is taken over thedistribution for idiosyncratic utility. Population mobility implies that this expected utility must equal thereservation level of utility in the the wider economy:

E [u] = γΦ1/ε = γ

[S∑r=1

S∑s=1

TrEs(drsQ

1−βr

)−ε(Brws)

ε

]1/ε

= U . (12)

A.2.3 Residence and Workplace Choices

Using the distribution of utility for pairs of blocks of residence and employment (6), the probability that aworker chooses the bilateral commute from i to j out of all possible bilateral commutes within the city is:

πij = Pr [uij ≥ maxurs; ∀r, s] ,

=

∫ ∞0

∏s 6=j

Gis(u)

[∏r 6=i

∏s

Grs(u)

]gij(u)du,

=

∫ ∞0

S∏r=1

S∏s=1

εΦiju−(ε+1)e−Φrsu−εdu.

=

∫ ∞0

εΦiju−(ε+1)e−Φu−εdu.

Note that:d

du

[− 1

Φe−Φu−ε

]= εu−(ε+1)e−Φu−ε . (13)

6

Using this result to evaluate the integral above, the probability that the worker chooses to live in block iand commute to work in block j is:

πij =TiEj

(dijQ

1−βi

)−ε(Biwj)

ε

∑Sr=1

∑Ss=1 TrEs

(drsQ

1−βr

)−ε(Brws)

ε≡ Φij

Φ. (14)

Therefore workers sort across residence and employment locations depending on their idiosyncratic prefer-ences and the characteristics of these locations. As discussed above, although we interpret the idiosyncraticshock as aecting utility, there is an isomorphic interpretation of the model in which the idiosyncratic shockapplies to eective units of labor. Therefore the endogenous sorting of workers across locations implies thatboth residence and employment locations dier in the composition of workers in terms of idiosyncraticdraws for utility or eective units of labor. Residential locations with higher values of Ti have higher aver-age draws of utility (or eective units of labor). Similarly, employment locations with higher values of Ejhave higher average draws of utility (or eective units of labor). To ensure that the general equilibrium ofthe model remains tractable, and because we do not observe worker characteristics in our data, we abstractfrom other dimensions of worker heterogeneity besides the idiosyncratic shock to preferences or eectiveunits of labor.

Summing across all possible employment locations s, we obtain the probability that a worker choosesto live in block i out of all possible locations within the city:

πRi =

∑Ss=1 TiEs

(disQ

1−βi

)−ε(Biws)

ε

∑Sr=1

∑Ss=1 TrEs

(drsQ

1−βr

)−ε(Brws)

ε≡ Φi

Φ. (15)

Similarly, summing across all possible residence locations r, we obtain the probability that a worker choosesto work in block j out of all possible locations within the city:

πMj =

∑Sr=1 TrEj

(drjQ

1−βr

)−ε(Brwj)

ε∑Sr=1

∑Ss=1 TrEs

(drsQ

1−βr

)−ε(Brws)

ε≡ Φj

Φ. (16)

For the measure of workers within block j (HMj), we can evaluate the conditional probability that theycommute from block i (conditional on having chosen to work in block j):

πij|j = Pr [uij ≥ maxusj;∀s] ,

=

∫ ∞0

∏s 6=i

Gsj(u)gij(u)du,

=

∫ ∞0

e−Φju−εεΦiju

−(ε+1)du.

Using the result (13) to evaluate the integral above, the probability that a worker commutes from block iconditional on having chosen to work in block j is:

πij|j =TiEj

(dijQ

1−βi

)−ε(Biwj)

ε

∑Sr=1 TrEj

(drjQ

1−βr

)−ε(Brwj)

ε=

Φij

Φj

,

7

which simplies to:

πij|j =Ti

(dijQ

1−βi

)−ε(Bi)

ε

∑Sr=1 Tr

(drjQ

1−βr

)−ε(Br)

ε. (17)

For the measure of residents within block i (HRi), we can evaluate the conditional probability that theycommute to block j (conditional on having chosen to live in block i):

πij|i = Pr [uij ≥ maxuis;∀s] ,

=

∫ ∞0

∏s 6=j

Gis(u)gij(u)du,

=

∫ ∞0

e−Φiu−εεΦiju

−(ε+1)du.

Using the result (13) to evaluate the integral above, the probability that a worker commutes to block j

conditional on having chosen to live in block i is:

πij|i =TiEj

(dijQ

1−βi

)−ε(Biwj)

ε

∑Ss=1 TiEs

(disQ

1−βi

)−ε(Biws)

ε=

Φij

Φi

,

which simplies to:

πij|i =Ej (wj/dij)

ε∑Ss=1Es (ws/dis)

ε. (18)

These conditional commuting probabilities provide microeconomic foundations for the reduced-formgravity equations estimated in the empirical literature on commuting patterns. The probability that a resi-dent of block i commutes to block j depends on the adjusted wage and commuting costs for block j in thenumerator (“bilateral resistance”) but also on the adjusted wage and commuting costs for all other possibleemployment locations s in the denominator (“multilateral resistance”).

Commuting market clearing requires that the measure of workers employed in each location j (HMj)equals the sum across all locations i of their measures of residents (HRi) times their conditional probabilitiesof commuting to j (πij|i):

HMj =S∑i=1

πij|iHRi (19)

=S∑i=1

Ej (wj/dij)ε∑S

s=1 Es (ws/dis)εHRi,

where, since there is a continuous measure of workers residing in each location, there is no uncertainty inthe supply of workers to each employment location.

Expected worker income conditional on living in block i is equal to the wages in all possible employment

8

locations weighted by the probabilities of commuting to those locations conditional on living in i:

E [ws|i] =S∑s=1

πis|iws, (20)

=S∑s=1

Es (ws/dis)ε∑S

r=1 Er (wr/dir)εws,

whereE denotes the expectations operator and the expectation is taken over the distribution for the idiosyn-cratic component of utility. Intuitively, expected worker income is high in blocks that have low commutingcosts (low dis) to high-wage employment locations.4

Finally, another implication of the Fréchet distribution of utility is that the distribution of utility condi-tional on residing in block i and commuting to block j is the same across all bilateral pairs of blocks withpositive residents and employment, and is equal to the distribution of utility for the city as a whole. Toestablish this result, note that the distribution of utility conditional on residing in block i and commutingto block j is given by:

1

πij

∫ u

0

∏s 6=j

Gis(v)

[∏r 6=i

∏s

Grs(v)

]gij(v)dv, (21)

=1

πij

∫ u

0

[S∏r=1

S∏s=1

e−Φrsv−ε

]εΦijv

−(ε+1)dv,

=Φ

Φij

∫ u

0

e−Φv−εεΦijv−(ε+1)dv,

=e−Φuε .

On the one hand, more attractive residential fundamentals in location i or a higher wage in location j raisethe utility of a worker with a given realization of idiosyncratic utility z, and hence increase the expectedutility of residing in i and working in j. On the other hand, more attractive residential fundamentals or ahigher wage induce workers with lower realizations of idiosyncratic utility z to reside in i and work in j,which reduces the expected utility of residing in i and working in j. With a Fréchet distribution of utility,these two eects exactly oset one another. Pairs of residence and employment locations with attractivefundamentals attract more commuters on the extensive margin until expected utility is the same across allpairs of residence and employment locations within the city.

A.2.4 Production

We follow the canonical urban model in assuming a single nal good that is costlessly traded within thecity and the larger economy.5 Final goods production occurs under conditions of perfect competition and

4For simplicity, we model agents and workers as synonymous, which implies that labor is the only source of income. Moregenerally, it is straightforward to extend the analysis to introduce families, where each worker has a xed number of dependentsthat consume but do not work, and/or to allow agents to have a constant amount of non-labor income.

5Even during division, there was substantial trade between West Berlin and West Germany. In 1963, the ratio of exportsto GDP in West Berlin was around 70 percent, with West Germany the largest trade partner. Overall, industrial productionaccounted for around 50 percent of West Berlin’s GDP in this year (American Embassy 1965).

9

constant returns to scale. For simplicity, we assume that the production technology takes the Cobb-Douglasform, so that output of the nal good in block j (yj) is:

yj = Aj (HMj)α (LMj)

1−α ,

where Aj is nal goods productivity; HMj is workplace employment; and LMj is oor space used commer-cially.

Firms choose their block of production and their inputs of workers and commercial oor space to max-imize prots, taking as given nal goods productivity (Aj), the distribution of idiosyncratic utility, goodsand factor prices, and the location decisions of other rms and workers. From the rst-order conditions forprot maximization, we obtain:

HMj =

(αAjwj

) 11−α

LMj. (22)

LMj =

((1− α)Aj

qj

) 1α

HMj. (23)

Therefore, employment in block j is increasing in productivity (Aj), decreasing in the wage (wj), and in-creasing in commercial land use (LMj). Similarly, commercial land use in block j is increasing in produc-tivity, decreasing in the commercial oor price (qj), and increasing in employment (HMj).

To determine the equilibrium commercial oor price, qj , we use the requirement that prots are zero ifthe nal good is produced:

Aj (HMj)α (LMj)

1−α − wjHMj − qjLMj = 0,

which together with prot maximization (22) yields the following expression for the equilibrium commercialoor price:

qj = (1− α)

(α

wj

) α1−α

A1

1−αj . (24)

Intuitively, blocks that have higher productivity (Aj) or lower wages (wj) are more attractive productionlocations, and hence must be characterized by higher commercial oor prices in an equilibrium in whichrms make zero prots in all locations with positive production.

A.2.5 Land Market Clearing

Land market equilibrium requires no-arbitrage between commercial and residential land use after takinginto the account the tax equivalent of land use regulations:

θi = 1 if qi > ξiQi,θi ∈ [0, 1] if qi = ξiQi,θi = 0 if qi < ξiQi,

(25)

where ξi ≥ 1 captures one plus the tax equivalent of land use regulations that restrict commercial land userelative to residential land use. We allow this wedge between commercial and residential oor prices tovary across blocks.

10

Therefore oor space in each block is either allocated entirely to commercial use (qi > ξiQi and θi = 1),allocated entirely to residential use (qi < ξiQi and θi = 0), or allocated to both uses (qi = ξiQi and θi ∈(0, 1)). We assume that the observed price of oor space in the data is the maximum of the commercial andresidential price of oor space: Qi = maxqi, Qi. Hence the relationship between observed, commercialand residential oor prices can be summarized as:

Qi = qi, qi > ξiQi, θi = 1,Qi = qi, qi = ξiQi, θi ∈ (0, 1),Qi = Qi, qi < ξiQi, θi = 0.

(26)

We follow the standard approach in the urban literature of assuming that oor space L is supplied by acompetitive construction sector that uses geographic land K and capital M as inputs. Following Combes,Duranton, and Gobillon (2014) and Epple, Gordon, and Sieg (2010), we assume that the production functiontakes the Cobb-Douglas form: Li = Mµ

i K1−µi .6 Therefore the corresponding dual cost function for oor

space is Qi = µ−µ(1 − µ)−(1−µ)PµR1−µi , where Qi = maxqi, Qi is the price for oor space, P is the

common price for capital, and Ri is the price for geographic land. Since the price for capital is the sameacross all locations, the relationships between the quantities and prices of oor space and geographical landarea can be summarized as:

Li = ϕiK1−µi (27)

Qi = χR1−µi , (28)

where ϕi = Mµi determines the density of development (the ratio of oor space to land area) and χ is a

constant.Residential land market clearing implies that the demand for residential oor space equals the supply

of oor space allocated to residential use in each location: (1− θi)Li. Using utility maximization for eachworker and taking expectations over the distribution for idiosyncratic utility, this residential land marketclearing condition can be expressed as:

E [`i]HRi = (1− β)E [ws|i]HRi

Qi

= (1− θi)Li. (29)

Commercial land market clearing requires that the demand for commercial oor space equals the supplyof oor space allocated to commercial use in each location: θjLj . Using the rst-order conditions for protmaximization, this commercial land market clearing condition can be written as:(

(1− α)Ajqj

) 1α

HMj = θjLj. (30)

When both residential and commercial land market clearing ((29) and (30) respectively) are satised, totaldemand for oor space equals the total supply of oor space:

(1− θi)Li + θiLi = Li = ϕiK1−µi . (31)

6Empirically, we nd that this Cobb-Douglas assumption is consistent with the micro data on property transactions for Berlinfrom 2000-2012, as shown in subsection A.11.6 of this web appendix.

11

A.2.6 Properties of General Equilibrium with Exogenous LocationCharacteristics

In this subsection, we characterize the properties of general equilibrium with exogenous location character-istics. In the next subsection, we relax these assumptions to allow for endogenous agglomeration forces.

We start with a benchmark case in which all locations have strictly positive, nite and exogenous loca-tion characteristics. In this benchmark case, we show that all locations are incompletely specialized withpositive values of both workplace and residence employment and positive shares of land allocated to com-mercial and residential use. We prove the existence of a unique general equilibrium for this benchmark caseof incomplete specialization.

We next allow some blocks to have zero workplace and/or residence employment, as observed empir-ically. We retain the assumption that location characteristics are exogenous. But we extend the analysisto allow for zero nal goods productivity and/or zero residential amenities. We show that a necessary andsucient condition for zero workplace employment in a block is zero nal goods productivity in that block.Similarly, a necessary and sucient condition for zero residence employment in a block is zero residentialamenities in that block. We extend our proof of the existence of a unique general equilibrium to allow forthese empirically relevant cases. Therefore, with exogenous location characteristics, the model has a uniquegeneral equilibrium.

Denition of Equilibrium: We now formally dene the general equilibrium of the model. Throughoutthe following, we use bold math font to denote vectors or matrices.

Denition A.1 Given the model’s parameters α, β, µ, ε, κ, λ, δ, η, ρ, the reservation level of utility in thewider economy U and exogenous location-specic characteristics T ,E,A,B,ϕ,K, ξ, τ, the general equi-librium of the model is referenced by the vector πM , πR, H ,Q, q, w, θ.

The seven elements of the equilibrium vector are determined by the following system of seven equations:

γ

[S∑r=1

S∑s=1

TrEs(drsQ

1−βr

)−ε(Brws)

ε

]1/ε

= U . (32)

πRi =

∑Ss=1 TiEs

(disQ

1−βi

)−ε(Biws)

ε

∑Sr=1

∑Ss=1 TrEs

(drsQ

1−βr

)−ε(Brws)

ε. (33)

πMi =

∑Sr=1 TrEi

(driQ

1−βr

)−ε(Brwi)

ε∑Sr=1

∑Ss=1 TrEs

(drsQ

1−βr

)−ε(Brws)

ε. (34)

θiLi =

((1− α)Ai

qi

) 1α

HMi. (35)

(1− θi)Li = (1− β)

[S∑s=1

Es (ws/dis)ε∑S

r=1Er (wr/dir)εws

]HRi

Qi

. (36)

12

qi = (1− α)

(α

wi

) α1−α

A1

1−αi . (37)

θi = 1 if qi > ξiQi,θi ∈ [0, 1] if qi = ξiQi,θi = 0 if qi < ξiQi,

(38)

where recall Li = ϕiK1−µi ; (32) is population mobility with the wider economy; (33) corresponds to the

residential choice probabilities; (34) corresponds to the workplace choice probabilities; (35) is commercialland market clearing; (36) is residential land market clearing; (37) corresponds to prot maximization andzero prots; (38) corresponds to no arbitrage between alternative uses of land.

Strictly Positive and Finite Exogenous Location Characteristics: We begin by considering a bench-mark case, in which all blocks have strictly positive, nite and exogenous location characteristics T ,E,A,B, ϕ, K , ξ, τ . We allow some blocks to be more attractive than others in terms of these characteristics.But workers draw idiosyncratic preferences from a Fréchet distribution for pairs of residence and workplacelocations. Therefore, since the support of the Fréchet distribution is unbounded from above, any block withstrictly positive characteristics has a positive measure of workers that prefer that location as a residenceor workplace at a positive and nite price. Hence, all blocks with nite positive wages attract a positivemeasure of workers, and all blocks with nite positive oor prices attract a positive measure of residents.

Lemma A.1 Assuming strictly positive, nite and exogenous location characteristics (Ti ∈ (0,∞), Ei ∈(0,∞), Ai ∈ (0,∞), Bi ∈ (0,∞), ϕi ∈ (0,∞), Ki ∈ (0,∞), ξi ∈ (0,∞), τij ∈ (0,∞) × (0,∞)), eachlocation i with a strictly positive and nite wage (wi ∈ (0,∞)) attracts a strictly positive measure of workers(HMi ∈ (0,∞)), and each location with a strictly positive and nite oor price (Qi ∈ (0,∞)) attracts a strictlypositive measure of residents (HRi ∈ (0,∞)).

Proof. Both properties follow immediately from the support of the Fréchet distribution being unboundedfrom above. For a strictly positive and nite wage (wi ∈ (0,∞)) for location i, there is a positive measure ofworkers who draw a large enough value of the idiosyncratic shock zri for each residence location r that theirpreferred workplace is i. Hence, from (18), the conditional probabilities of commuting from each residencelocations r to workplace i are strictly positive for wi ∈ (0,∞). Additionally, for a strictly positive and niteoor price (Qi ∈ (0,∞)) for location i, there is a positive measure of workers who draw a large enoughvalue of the idiosyncratic shock zis that their preferred residence is i for each workplace s. Therefore,from (17), the conditional probabilities of commuting from i to each workplace s are strictly positive forQi ∈ (0,∞).

We next show that blocks with strictly positive, nite and exogenous location characteristics T ,E,A,B,ϕ,K , ξ, τ must have strictly positive and nite values of both wages and oor prices in equilibrium. Thereason is that the utility and production function satisfy the Inada conditions. Therefore, given a positivemeasure of workers, the return to commercial land use becomes large as the fraction of land allocated tocommercial use becomes small. Similarly, given a positive measure of residents, the return to residential

13

land use becomes large as the fraction of land allocated to residential use becomes small. Since locationsattract positive measures of workers and residents at any nite positive wage and oor price, it follows thatpositive fractions of land must be allocated to both commercial and residential use.

Lemma A.2 Assuming strictly positive, nite and exogenous location characteristics (Ti ∈ (0,∞), Ei ∈(0,∞), Ai ∈ (0,∞), Bi ∈ (0,∞), ϕi ∈ (0,∞), Ki ∈ (0,∞), ξi ∈ (0,∞), τij ∈ (0,∞) × (0,∞)), alllocations are incompletely specialized and allocate positive fractions of land to commercial and residential use:θi ∈ (0, 1).

Proof. This property follows from the support of the Fréchet distribution being unbounded from aboveand from the utility and production functions both satisfying the Inada conditions. Lemma A.1 implies thateach location with strictly positive and nite wages (wi ∈ (0,∞)) attracts a strictly positive measure ofworkers (HMi ∈ (0,∞)). But prot maximization and commercial land market clearing imply:

qi = (1− α)Ai

(HMi

θiLi

)α,

which in turn implies (i) limθi→0 qi = ∞ for Ai ∈ (0,∞) and HMi ∈ (0,∞); (ii) qi ∈ (0,∞) for allθi ∈ (0, 1], Ai ∈ (0,∞) and HMi ∈ (0,∞). Therefore a positive fraction of land must be allocated tocommercial use: θi > 0. Additionally, Lemma A.1 implies that each location with strictly positive and nitevalues of both amenities (Bi ∈ (0,∞)) and oor prices (Qi ∈ (0,∞)) attracts a strictly positive measure ofresidents (HRi ∈ (0,∞)). But utility maximization and residential land market clearing imply:

Qi = (1− β)

[S∑s=1

Es (ws/dis)ε∑S

r=1 Er (wr/dir)εws

]HRi

(1− θi)Li,

which in turn implies (i) lim(1−θi)→0Qi =∞ for HRi ∈ (0,∞); (ii) Qi ∈ (0,∞) for all (1− θi) ∈ (0, 1] andHRi ∈ (0,∞). Therefore a positive fraction of land must be allocated to residential use: (1− θi) > 0.

Having shown that the assumption of strictly positive, nite and exogenous location characteristicsimplies incomplete specialization, we are now in a position to establish the following proposition.

Proposition A.1 Assuming strictly positive, nite and exogenous location characteristics (Ti ∈ (0,∞), Ei ∈(0,∞), Ai ∈ (0,∞), Bi ∈ (0,∞), ϕi ∈ (0,∞), Ki ∈ (0,∞), ξi ∈ (0,∞), τij ∈ (0,∞) × (0,∞)), thereexists a unique general equilibrium vector πM , πR, H ,Q, q, w, θ.

Proof. With strictly positive, nite and exogenous location characteristics (Ti ∈ (0,∞), Ei ∈ (0,∞),Ai ∈ (0,∞), Bi ∈ (0,∞), ϕi ∈ (0,∞), Ki ∈ (0,∞), ξi ∈ (0,∞), τij ∈ (0,∞) × (0,∞)), locations areincompletely specialized and the no-arbitrage condition between alternative uses of land (25) holds, whichimplies that commercial oor prices can be expressed in terms of residential oor prices: qi = ξiQi. Usingthis result together with the probability of residing in a location (15), the probability of working in a location

14

(16), the zero-prot condition (24), and the indierence condition between the city and the larger economy(12), the fraction of the city’s population residing in location i can be written as:

πRi =HRi

H=( γU

)ε S∑s=1

TiEs

(disQ

1−βi

)−ε (Bi(1− α)

1−αα αA

1αs

)ε(ξsQs)

− ε(1−α)α ,

while the fraction of the city’s population working in location i can be written as:

πMi =HMi

H=( γU

)ε S∑s=1

TsEi(dsiQ

1−βs

)−ε (Bs(1− α)

1−αα αA

1αi

)ε(ξiQi)

− ε(1−α)α ,

and expected worker income conditional on residing in block i (20) can be written as:

E [ws|i] =S∑s=1

Es

(A

1αs (ξsQs)

− 1−αα /dis

)ε∑S

r=1 Er

(A

1αr (ξrQr)

− 1−αα /dir

)ε [(1− α)1−αα αA

1αs (ξsQs)

− 1−αα

].

Using commercial land market clearing (30) and residential land market clearing (29), the requirement thatthe land market clears can be written as:(

(1− α)AiξiQi

) 1α

πMi + (1− β)E [ws|i]Qi

πRi =LiH.

Combining the above relationships, the land market clearing condition can be written as:

Di(Q) =(

(1−α)AiξiQi

) 1α ∑S

s=1 TsEi

(Bs(1−α)

1−αα αA

1αi

dsiQ1−βs (ξiQi)

1−αα

)ε+ (1−β)

Qi

∑Ss=1

Es

(A

1αs (ξsQs)

− 1−αα /dis

)ε∑Sr=1 Er

(A

1αr (ξrQr)

− 1−αα /dir

)ε [( 1−αξsQs

)1−αα αA

1αs

]∑Ss=1 TiEs

(Bi(1−α)

1−αα αA

1αs

disQ1−βi (ξsQs)

1−αα

)ε= Li,

for all i, where we have chosen units in which to measure utility so that (U/γ)ε/H = 1. The above landmarket clearing condition provides a system of S equations in the S unknown residential oor prices Qi

for each location i, which has the following properties:

limQi→0

Di(Q) =∞ > Li, limQi→∞

Di(Q) = 0 < Li,

dDi(Q)

dQi

< 0,dDi(Q)

dQj

< 0,

∣∣∣∣dDi(Q)

dQi

∣∣∣∣ > ∣∣∣∣dDi(Q)

dQj

∣∣∣∣ .It follows that there exists a unique vector of residential oor prices Q that solves this system of landmarket clearing conditions. Commercial oor prices follow immediately from q = ξQ. Having solved forthe vectors of oor prices Q, q, the vector of wagesw follows immediately from the zero-prot conditionfor production (24). Given oor prices Q, q and wages (w), the probability of residing in a location (πR)follows immediately from (15), and the probability of working in a location (πM ) follows immediatelyfrom (16). Having solved for πM , πR, Q, q, w, the total measure of workers residing in the city can

15

be recovered from our choice of units in which to measure utility (U/γ)ε/H = 1), which together withpopulation mobility (12) implies:

H =

[S∑r=1

S∑s=1

TrEs(drsQ

1−βr

)−ε(Brws)

ε

].

We therefore obtain HM = πMH and HR = πRH . Given oor prices Q, q and employments HM ,HR, the fraction of land that is used commercially (θ) follows immediately from commercial and residentialland market clearing. This completes the determination of the equilibrium vector πM , πR, H ,Q, q,w, θ.

Allowing for Zero Workplace and/or Residence Employment: A corollary of lemmas A.1 and A.2is that a necessary and sucient condition for zero workplace employment and zero commercial land usein a block is zero nal goods productivity. Similarly, a necessary and sucient condition for zero residenceemployment and zero residential land use in a block is zero amenities.

Lemma A.3 Assuming strictly positive, nite and exogenous location characteristics (Ti ∈ (0,∞), Ei ∈(0,∞), ϕi ∈ (0,∞), Ki ∈ (0,∞), ξi ∈ (0,∞), τij ∈ (0,∞)× (0,∞)):(i) a necessary and sucient condition for zero workplace employment (HMi = 0) and zero commercial landuse (θi = 0) is zero nal goods productivity (Ai = 0) for location i,(ii) a necessary and sucient condition for zero residence employment (HRi = 0) and zero residential land use((1− θi) = 0) is zero amenities (Bi = 0) for location i.

Proof. From lemma A.1 and the conditional probability of commuting to location i conditional on living ineach residence location r (18), a necessary and sucient condition for HMi = 0 for workplace i is wi = 0.From the rst-order conditions for prot maximization (22) and (23), a necessary and sucient condition forwi = 0 and θi = 0 isAi = 0. From lemma A.1 and the conditional probability of commuting from location iconditional on working in each workplace s (17), a necessary and sucient condition forHRi = 0 isBi = 0.From residential land market clearing (29), a necessary and sucient condition for (1− θi) = 0 is HRi = 0,which is ensured by Bi = 0.

From lemma A.3, a necessary and sucient condition for a block to have both no commercial activityand no residential activity is Ai = 0 and Bi = 0. Such blocks with no economic activity play no directrole in the model but aect the general equilibrium in so far as they aect travel times (τij) between blockswith positive economic activity. We now use the results from lemma A.3 to generalize Proposition A.1 toprove that there exists a unique equilibrium given exogenous location characteristics once we allow blocksto have no commercial activity and/or no residential activity.

From (26), lemmas A.1-A.3 and no-arbitrage between alternative uses of land, we can summarize therelationships between the observed price of oor space (Qi), the price of commercial oor space (qi), the

16

residential price of oor space (Qi), and land use as:

Qi =

ζMiqi, ζMi = 1, i ∈ =M = Ai > 0, Bi = 0,ζMiqi, ζMi = 1, i ∈ =S = Ai > 0, Bi > 0. (39)

Qi =

ζRiQi, ζRi = 1, i ∈ =R = Ai = 0, Bi > 0,ζRiQi, ζRi = ξi, i ∈ =S = Ai > 0, Bi > 0.

where ζMi and ζRi relate observed oor prices to commercial and residential oor prices respectively; =Mis the set of locations specialized in commercial activity (θi = 1); =S is the set of locations with bothcommercial and residential activity (θi ∈ (0, 1)); and =R is the set of locations specialized in residentialactivity (θi = 0).

From (39), these relationships between the observed, commercial and residential prices of oor spaceQi, qi,Qi, and the allocation of land between commercial and residential use θi, 1−θi, are a function solelyof the exogenous locational characteristics A, B, ξ. We now use this property to generalize PropositionA.1 to allow blocks to have no commercial activity and/or residential activity.

Proposition A.2 Assuming exogenous, nite and strictly positive location characteristics (Ti ∈ (0,∞), Ei ∈(0,∞), ϕi ∈ (0,∞), Ki ∈ (0,∞), ξi ∈ (0,∞), τij ∈ (0,∞) × (0,∞)), and exogenous, nite and non-negative nal goods productivity Ai ∈ [0,∞) and residential amenities Bi ∈ [0,∞), there exists a uniquegeneral equilibrium vector πM , πR, H ,Q, q, w, θ.

Proof. The proof follows a similar structure as for Proposition A.1. For locations that are completelyspecialized in commercial activity (i ∈ =M ), the land market clearing condition can be written,

Di(Q) =(

(1−α)AiQi

) 1α ∑s∈=S∪=R

TsEi

(Bs(1−α)

1−αα αA

1αi

dsi(Qs/ζRs)1−β(Qi)1−αα

)ε= Li.

For locations that are incompletely specialized in commercial and residential activity (i ∈ =S), the landmarket clearing condition can be written:

Di(Q) =(

(1−α)AiQi

) 1α ∑s∈=S∪=R

(T

1/εs E

1/εi Bs(1−α)

1−αα αA

1αi

dsi(Qs/ζRs)1−β(Qi)1−αα

)ε+ (1−β)

Qi/ζRi

∑s∈=M∪=S

Es

(A

1αs (Qs)−

1−αα /dis

)ε[((1−α)Qs

)1−αα αA

1αs

]∑

r∈=M∪=SEr

(A

1αr (Qr)−

1−αα /dir

)ε ∑s∈=M∪=S

(T

1/εi E

1/εs Bi(1−α)

1−αα αA

1αs

dis(Qi/ζRi)1−β(Qs)1−αα

)ε= Li.

For locations that are completely specialized in residential activity (i ∈ =R), the land market clearingcondition can be written:

Di(Q) = (1−β)Qi/ζRi

∑s∈=M∪=S

Es

(A

1αs (Qs)−

1−αα /dis

)ε[((1−α)Qs

)1−αα αA

1αs

]∑Sr=1 Er

(A

1αr (Qr)−

1−αα /dir

)ε ∑s∈=M∪=S

(T

1/εi E

1/εs Bi(1−α)

1−αα αA

1αs

dis(Qi/ζRi)1−β(Qs)1−αα

)ε= Li.

We have again chosen units in which to measure utility so that (U/γ)ε/H = 1. The above land marketclearing conditions provide a system of S equations in the S unknown observed oor prices Qi for eachlocation i, which has the following properties:

limQi→0

Di(Q) =∞ > Li, limQi→∞

Di(Q) = 0 < Li,

17

dDi(Q)

dQi

< 0,dDi(Q)

dQj

< 0,

∣∣∣∣dDi(Q)

dQi

∣∣∣∣ > ∣∣∣∣dDi(Q)

dQj

∣∣∣∣ .It follows that there exists a unique vector of observed oor prices Q that solves this system of land marketclearing conditions. Having determined Q, commercial oor prices (q) and residential oor prices (Q)follow immediately from the relationship between oor prices (39) as a function of the exogenous locationcharacteristics A,B, ξ. The remainder of the equilibrium vector follows from exactly the same argumentsas for Proposition A.1.

We use Proposition A.2 to undertake counterfactuals for division and reunication, in which we treatlocation characteristics as exogenous and hold them constant at their values before division or reunica-tion. Since the model features a unique equilibrium with exogenous location characteristics, these coun-terfactuals yield determinate predictions for the impact of division and reunication on the organization ofeconomic activity within the city.

A.2.7 Properties of General Equilibrium with Agglomeration Forces

We now relax the assumption that productivity (Ai) and amenities (Bi) are exogenous. We examine howthe introduction of endogenous agglomeration forces aects the properties of the general equilibrium ofthe model. We decompose productivity (Ai) and amenities (Bi) into two components, one of which isexogenous and captures location fundamentals, and the other of which is endogenous to the surroundingconcentration of economic activity and captures agglomeration forces.

Agglomeration Forces: We allow nal goods productivity to depend on production fundamentals (aj)and production externalities (Υj). Production fundamentals capture features of physical geography thatmake a location more or less productive independently of the surrounding density of economic activity(for example access to natural water). Production externalities impose structure on how the productivityof a given block is aected by the characteristics of other blocks. Specically, we follow the standard ap-proach in urban economics of modeling these externalities as depending on the travel-time weighted sumof workplace employment density in surrounding blocks:7

Aj = ajΥλj , Υj ≡

S∑s=1

e−δτjs(HMs

Ks

), (40)

where HMs/Ks is workplace employment density per unit of geographical land area; production externali-ties decline with travel time (τjs) through the iceberg factor e−δτjs ∈ (0, 1]; δ determines their rate of spatialdecay; and λ controls their relative importance in determining overall productivity.8

7While the canonical interpretation of these production externalities in the urban economics literature is knowledge spillovers,as in Alonso (1964), Fujita and Ogawa (1982), Lucas (2000), Mills (1967), Muth (1969), and Sveikauskas (1975), other interpretationsare possible, as considered in Duranton and Puga (2004).

8We make the standard assumption that production externalities depend on employment density per unit of geographicalland area Ki (rather than per unit of oor space Li) to capture the role of higher ratios of oor space to geographical land areain increasing the surrounding concentration of economic activity.

18

We model the externalities in workers’ residential choices analogously to the externalities in rms’ pro-duction choices. We allow residential amenities to depend on residential fundamentals (bi) and residentialexternalities (Ωi). Residential fundamentals capture features of physical geography that make a location amore or less attractive place to live independently of the surrounding density of economic activity (for ex-ample green areas). Residential externalities again impose structure on how the amenities in a given blockare aected by the characteristics of other blocks. Specically, we adopt a symmetric specication as forproduction externalities, and model residential externalities as depending on the travel-time weighted sumof residential employment density in surrounding blocks:

Bi = biΩηi , Ωi ≡

S∑r=1

e−ρτir(HRr

Kr

), (41)

whereHRr/Kr is residence employment density per unit of geographical land area; residential externalitiesdecline with travel time (τir) through the iceberg factor e−ρτir ∈ (0, 1]; ρ determines their rate of spatialdecay; and η controls their relative importance in overall residential amenities.

Equilibrium Properties with Agglomeration Forces: We begin by establishing some properties ofthe general equilibrium of the model with agglomeration forces. Production externalities (Υj) are modeledas the travel time weighted sum of workplace employment density throughout the city. Therefore, sincetravel time within Berlin is nite, production externalities are strictly positive for all blocks for a nite spatialdecay of production externalities (δ), as long as workplace employment is positive somewhere within Berlin:Υj > 0 for all j ∈ 1, . . . , S if HMs > 0 for some s ∈ 1, . . . , S and 0 < δ < ∞. Similarly, residentialexternalities (Ωi) are modeled as the travel time weighted sum of residence employment density throughoutthe city. Therefore, since travel time within Berlin is nite, residential externalities are strictly positive forall blocks for a nite spatial decay of residential externalities (ρ), as long as residence employment is positivesomewhere within Berlin: Ωi > 0 for all i ∈ 1, . . . , S ifHRs > 0 for some s ∈ 1, . . . , S and 0 < ρ <∞.

We now combine this result that production and residential externalities are strictly positive and nitewith the properties that (i) the support of the Fréchet distribution is unbounded from above and (ii) the utilityand production functions satisfy the Inada conditions. From these results, if all location characteristicsare strictly positive for all blocks, it follows that all blocks will be incompletely specialized with positivefractions of land allocated to commercial and residential use. We therefore have the following generalizationof Lemmas A.1 and A.2 to the case of endogenous agglomeration forces.

Lemma A.4 Assume (i) strictly positive, nite and exogenous location fundamentals (Ti ∈ (0,∞), Ei ∈(0,∞), ai ∈ (0,∞), bi ∈ (0,∞), ϕi ∈ (0,∞), Ki ∈ (0,∞), ξi ∈ (0,∞), τij ∈ (0,∞) × (0,∞)), (ii)endogenous agglomeration forces (λ, η > 0), (iii) nite spatial decays of agglomeration externalities (0 < δ <

∞ and 0 < ρ <∞):(i) Each location i with a strictly positive and nite wage (wi ∈ (0,∞)) attracts a strictly positive measure ofworkers (HMi ∈ (0,∞)), and each location with a strictly positive and nite oor price (Qi ∈ (0,∞)) attractsa strictly positive measure of residents (HRi ∈ (0,∞)).

19

(ii) Any equilibrium with positive workplace and residence employment somewhere in the city (HMj, HRi > 0

for some j, i ∈ 1, . . . , S) is characterized by incomplete specialization, with all locations allocating positivefractions of land to commercial and residential use: θi ∈ (0, 1).

Proof. The proof of the lemma follows exactly the same structure as the proof of Lemmas A.1 and A.2above. Since the support of the Fréchet distribution is unbounded from above, any location with strictlypositive and nite wages (wi ∈ (0,∞)) attracts a strictly positive measure of workers (HMi ∈ (0,∞)). Butprot maximization and commercial land market clearing imply:

qi = (1− α)aiΥλi

(HMi

θiLi

)α,

which in turn implies (i) limθi→0 qi =∞ for ai ∈ (0,∞), Υi ∈ (0,∞) andHMi ∈ (0,∞); (ii) qi ∈ (0,∞) forall θi ∈ (0, 1], ai ∈ (0,∞), Υi ∈ (0,∞) andHMi ∈ (0,∞). Therefore a positive fraction of land is allocatedto commercial use: θi > 0. Additionally, each location with strictly positive and nite values of residentialfundamentals (bi ∈ (0,∞)), residential externalities (Ωi ∈ (0,∞)) and oor prices (Qi ∈ (0,∞)) attracts astrictly positive measure of residents (HRi ∈ (0,∞)). But utility maximization and residential land marketclearing imply:

Qi = (1− β)

[S∑s=1

Es (ws/dis)ε∑S

r=1 Er (wr/dir)εws

]HRi

(1− θi)Li,

which in turn implies (i) lim(1−θi)→0Qi =∞ for HRi ∈ (0,∞); (ii) Qi ∈ (0,∞) for all (1− θi) ∈ (0, 1] andHRi ∈ (0,∞). Therefore a positive fraction of land is allocated to residential use: (1− θi) > 0.

Since production externalities are strictly positive (Υi > 0), an immediate corollary of Lemma A.4 isthat a necessary and sucient condition for zero workplace employment and zero commercial land usein a block is zero production fundamentals (ai = 0). Similarly, since residential externalities are strictlypositive (Ωi > 0), an immediate corollary of Lemma A.4 is that a necessary and sucient condition for zeroresidence employment and zero residential land use in a block is zero residential fundamentals (bi = 0).

Lemma A.5 Assume (i) strictly positive, nite and exogenous location characteristics (Ti ∈ (0,∞), Ei ∈(0,∞), ϕi ∈ (0,∞), Ki ∈ (0,∞), ξi ∈ (0,∞), τij ∈ (0,∞)× (0,∞)), (ii) endogenous agglomeration forces(λ, η > 0), (iii) nite spatial decays of agglomeration externalities (0 < δ < ∞ and 0 < ρ < ∞). In anyequilibrium with positive workplace and residence employment somewhere in the city (HMj, HRi > 0 for somej, i ∈ 1, . . . , S):(i) a necessary and sucient condition for zero workplace employment (HMi = 0) and zero commercial landuse (θi = 0) is zero production fundamentals (ai = 0) for location i,(ii) a necessary and sucient condition for zero residence employment (HRi = 0) and zero residential land use((1− θi) = 0) is zero residential fundamentals (bi = 0) for location i.

Proof. From lemma A.4 and the conditional probability of commuting to location i conditional on living ineach residence location r (18), a necessary and sucient condition for HMi = 0 for workplace i is wi = 0.

20

From the rst-order conditions for prot maximization (22) and (23), a necessary and sucient condition forwi = 0 and θi = 0 is Ai = 0. From the productivity specication (40), a necessary and sucient conditionfor Ai = 0 is ai = 0 since Υi > 0. From lemma A.4 and the conditional probability of commuting fromlocation i conditional on working in each workplace s (17), a necessary and sucient condition forHRi = 0

is Bi = 0. From residential land market clearing (29), a necessary and sucient condition for (1− θi) = 0

is HRi = 0, which is ensured by Bi = 0. From the amenities specication (41), a necessary and sucientcondition for Bi = 0 is bi = 0 since Ωi > 0.

Potential forMultiple Equilibria: As is standard in urban models, the presence of endogenous agglom-eration forces introduces the potential for multiple equilibria into the model: Each agent’s location decisiondepends on productivity and amenities, but productivity and amenities in turn depend on the location deci-sions of all agents. Whether or not multiple equilibria exist depends on the strength of these agglomerationforces relative to the size of the exogenous dierences in location characteristics (T , E, a, b, ϕ, K , ξ, τ ).The strength of agglomeration forces depends on both their contribution to productivity and amenities (λ,η) and their spatial decay with travel times (δ, ρ). An important feature of our empirical approach is that itexplicitly addresses the potential for multiple equilibria, as discussed further in Sections A.3 and A.5 of thisweb appendix (see, in particular, Propositions A.3 and A.4 and subsection A.5.5).

A.3 Calibration

We now show that there is a unique mapping from the observed variables to unobserved values of locationcharacteristics. These unobserved location characteristics include production and residential fundamentalsand several other unobserved variables. Since a number of these unobserved variables enter the modelisomorphically, we dene the following composites denoted by a tilde:

Ai = AiEα/εi , ai = aiE

α/εi ,

Bi = BiT1/εi ζ1−β

Ri , bi = biT1/εi ζ1−β

Ri ,

wi = wiE1/εi ,

ϕi = ϕi

(ϕi, E

1/εi , ξi

),

where we use i to index all blocks; the function ϕi (·) is dened below; ζRi = 1 for completely specializedresidential blocks; and ζRi = ξi for residential blocks with some commercial land use.

In the labor market, the adjusted wage (wi) captures the wage (wi) and the Fréchet scale parameter foreach employment location (E1/ε

i ), because these both aect the relative attractiveness of an employmentlocation to workers. On the production side, adjusted productivity (Ai) captures productivity (Ai) andthe Fréchet scale parameter for each employment location (Eα/ε

i ), because these both aect the adjustedwage consistent with zero prots. Adjusted production fundamentals are dened analogously. On theconsumption side, adjusted amenities (Bi) capture amenities (Bi), the Fréchet scale parameter for eachresidence location (T 1/ε

i ), and the wedge between commercial and residential oor prices (ξi), because these

21

all aect the relative attractiveness of a location consistent with population mobility. Adjusted residentialfundamentals are dened analogously. Finally, in the land market, the adjusted density of development (ϕi)includes the density of development (ϕ) and other production and residential parameters that aect theequality of the demand and supply for oor space, as shown below.

In the remainder of this section, we show how the model can be calibrated to recover unique adjusted lo-cation characteristics given known values of the model’s parameters α, β, µ, ε, κ, λ, δ, η, ρ and the observeddata Q,HR,HM ,K , τ . We show that there is a one-to-one mapping from these known parameters andthe observed data to the adjusted location characteristics ai, bi, ϕi. Therefore these unobserved adjustedlocation characteristics correspond to structural residuals of the model that are one-to-one functions of theparameters and the observed data. We use the resulting closed-form solutions for these structural residualsto construct moment conditions in the structural estimation of the model in Section A.5, where both theparameters α, β, µ, ε, κ, λ, δ, η, ρ and the unobserved adjusted location characteristics ai, bi, ϕi areunknown and to be estimated.

In addition to establishing the one-to-one mapping from the parameters and observables to the unob-servables, we show that the model has a recursive structure. Given a subset of the model’s parameters α, β,µ, ε, κ, there is a one-to-one mapping from these parameters and the observed data Q,HR,HM ,K , τ tothe unobserved adjusted location characteristics Ai, Bi, ϕi. Therefore, overall adjusted productivity (Ai),overall adjusted amenities (Bi) and the adjusted density of development (ϕi) can be uniquely determinedirrespective of whether they are exogenous or endogenous. Furthermore, overall adjusted productivity(Ai) and amenities (Bi) can be determined irrespective of the relative importance of their components ofexternalities Υi,Ωi and adjusted fundamentals ai, bi.

A.3.1 Determining A, B, ϕ from α, β, µ, ε, κ and the Observed Data

We begin by establishing the one-to-one mapping from the subset of the parameters α, β, µ, ε, κ and theobserved data Q,HR,HM ,K , τ to adjusted nal goods productivity, residential amenities and the densityof development A, B, ϕ. To do so, we use the recursive structure of the model.

1. Given ε, κ and the observed data HR, HM , τ , the equilibrium adjusted wage vector w can beuniquely determined from the commuting market clearing condition alone independently of the otherequilibrium conditions of the model.

2. Given ε, κ, β, µ, the observed data Q, HR, HM , τ and adjusted wages w, adjusted residentialamenities B can be uniquely determined from residential choice probabilities.

3. Given ε, κ, α, µ, the observed data Q, HR, HM , τ and adjusted wages w, adjusted nal goodsproductivity A can be uniquely determined from prot maximization and zero prots.

4. Given ε, κ, α, β, µ, the observed data Q,HR,HM ,K , τ , and adjusted wages and productivity w,A, the adjusted density of development ϕ can be uniquely determined from land market clearing.

In the remainder of this subsection, we consider each of these steps in turn.

22

A.3.1.1 Wages

Given the parameters ε, κ and observed data HM ,HR, τ, commuting market clearing (19) provides asystem of equations in observed workplace and residence employment that determines a unique adjustedwage vector (w) up to a normalization (a choice of units in which to measure wages):

HMj =S∑i=1

(E

1/εj wj/e

κτij

)ε∑S

s=1

(E

1/εs ws/eκτis

)εHRi, (42)

=S∑i=1

(wj/eκτij)ε∑S

s=1 (ws/eκτis)εHRi.

Adjusted wages (wj = E1/εj wj) capture (i) wages (wj) in employment location j and (ii) the Fréchet scale

parameter that determines the average utility (or eective units of labor) for commuters to that employ-ment location (Ej). Note that E1/ε

j enters the commuting market clearing condition isomorphically to wj .Therefore only the composite adjusted wage (wj) can be recovered from the data. From lemmas A.1-A.3, alllocations with zero workplace employment have zero adjusted wages.

We now show that this commuting market clearing condition determines a unique adjusted wage (wj)for each location j = 1, . . . , S. Note that the commuting market clearing condition (42) can be re-writtenas the following excess demand system:

Dj (w) = HMj −S∑i=1

(wj/dij)ε∑S

s=1 (ws/dis)εHRi = 0, dij = eκτij . (43)

We use HM ∈ <S+ to denote the observed non-negative vector of workplace employment with elementsHMj given by the data;HR ∈ <S+ denotes the observed non-negative vector of residence employment withelements HRi, given by the data; τij ∈ <S+×<S+ denotes the observed bilateral travel time between blocks iand j; and w ∈ <S+ is the unknown non-negative adjusted wage vector with elements wj . The system (43)captures the requirement of zero excess demand for commuters at the adjusted wage vector w.

Lemma A.6 Given the parameters ε, κ and observables HM , HR, τ , the wage system (43) exhibits thefollowing properties in w:Property (i): D(w) is continuous.Property (ii): D(w) is homogenous of degree zero.Property (iii):

∑j∈S Dj (w) = 0 for all w ∈ <S+.

Property (iv): D(w) exhibits gross substitution:

∂Dj (w)

∂wk> 0 for all j, k, j 6= k for all w ∈ <S+,

∂Dj (w)

∂wj< 0 for all j for all w ∈ <S+.

23

Proof. Property (i) follows immediately by inspection of (43).Property (ii) follows immediately by inspection of (43).Property (iii) can be established by noting:

S∑j=1

Dj (w) =S∑j=1

HMj −S∑i=1

∑Sj=1 (wj/dij)

ε∑Ss=1 (ws/dis)

εHRi

=S∑j=1

HMj −S∑i=1

HRi

= 0.

Property (iv) can be established by noting:

∂Dj (w)

∂wk=∑i∈S

(wj/dij)ε ε (wk/dik)

ε w−1k[∑

s∈S (ws/dis)ε]2 HRi > 0.

and using homogeneity of degree zero, which implies:

∇D (w) w = 0,

and hence:∂Dj (w)

∂wj< 0 for all j for all w ∈ <S+.

Therefore we have established gross substitution.

Lemma A.7 Given the parameters ε, κ and observed data HM ,HR, τ , there exists a unique adjusted wagevector w∗ ∈ <S+ such that D(w∗) = 0.

Proof. We rst show that the adjusted wage system D (w) has at most one (normalized) solution usingthe properties established in Lemma A.6. Gross substitution implies that D (w) = D (w′) cannot occurwhenever w and w′ are two adjusted wage vectors that are not colinear. By homogeneity of degree zero,we can assume w′ ≥ w and wj = w′j for some j. Now consider altering the adjusted wage vector w′ toobtain the adjusted wage vector w in S − 1 steps, lowering (or keeping unaltered) the adjusted wage of allthe other S−1 locations k 6= j one at a time. By gross substitution, the excess demand for labor in locationj cannot decrease in any step, and because w 6= w′, it will actually increase in at least one step. HenceDj (w) > Dj (w′) and we have a contradiction.

We next establish that there exists an adjusted wage vector w∗ ∈ <S+ such that D(w∗) = 0. By ho-mogeneity of degree zero, we can restrict our search for an equilibrium adjusted wage vector to the unitsimplex ∆ =

w ∈ <S+ :

∑Sj=1 wj = 1

. Dene on ∆ the function D+ (·) by D+

j (w) = max Dj (w) , 0.Note that D+ (·) is continuous. Denote α (w) =

∑Sj=1

[wj +D+

j (w)]. We have α (w) ≥ 1 for all w.

Dene a continuous function f (·) from the closed convex set ∆ into itself by:

f (w) = [1/α (w)][w +D+ (w)

].

24

Note that this xed-point function tends to increase the wages of locations with excess demand for com-muters. By Brouwer’s Fixed-point Theorem, there exists w∗ ∈ ∆ such that w∗ = f (w∗).

Since∑S

j=1 Dj (w) = 0, it cannot be the case that Dj (w) > 0 for all j = 1, . . . , S or Dj (w) < 0 forall j = 1, . . . , S. Additionally, if Dj (w) > 0 for some j and Dk (w) < 0 for some k 6= j, w 6= f (w). Itfollows that at the xed point for wages, w∗ = f (w∗), and Dj (w) = 0 for all j.

Homogeneity of degree zero of the commuting market clearing condition (42) implies that the equilib-rium adjusted wage vector is unique up to a normalization. We impose the normalization that the geometric

mean adjusted wage is equal to one ([∏S

j=1 wjt

] 1S

= 1), as discussed further in subsection A.3.1.5 below.In our estimation, it proves convenient to re-write the commuting market clearing condition (42) in

terms of a composite parameter ν = εκ that captures the semi-elasticity of commuting ows with respectto travel times and a transformation of adjusted wages (ωjt = wεjt = Ejtw

εjt):

HMjt =S∑i=1

ωjt/eντijt∑S

s=1 ωst/eντist

HRit. (44)

The commuting market clearing condition (44) exhibits the same properties in transformed wages (ωjt) asestablished for adjusted wages (wjt) in Lemmas A.6 and A.7 above.

A.3.1.2 Adjusted Residential Amenities

Given the parameters β, µ, ε, κ, observed data Q,HM ,HR, τ and the above solutions for adjustedwages w, the residential choice probabilities (15) and population mobility (12) determine a unique vectorof adjusted residential amenities (B) up to a normalization. From the residential choice probabilities (15)and population mobility (12), we have:

BiT1/εi

U/γ=

(HRi

H

) 1ε Q1−β

i

W1/εi

,

where Wi is a measure of commuting market access:

Wi =S∑s=1

Es (ws/dis)ε , dis = eκτis .

and these expressions can be equivalently rewritten as:

Bi

U/γ=

(HRi

H

) 1ε Q1−β

i

W1/εi

, (45)

Wi =S∑s=1

(ws/dis)ε , dis = eκτis . (46)

For locations s ∈ =S ∪ =R with positive residence employment, residential oor prices are related toobserved oor prices through Qs = ζRsQs, where (i) ζRs = ξs if s ∈ =S and (ii) ζRs = 1 if s ∈ =R.

25

Adjusted residential amenities (Bi = BiT1/εi ζ1−β

Ri ) include (i) residential amenities (Bi), (ii) the Fréchet scaleparameter (Ti) that determines the average utility (or eective units of labor) for commuters from locationi, and (iii) the relationship between observed and residential oor prices (ζRi). The parameter ζRi capturesland use regulations that introduce a wedge between commercial and residential oor prices (ξi), where weallow this wedge (ξi) to vary across blocks. Note that T 1/ε

i and ζ1−βRi enter residential choice probabilities

isomorphically to Bi. Therefore only the composite adjusted residential amenities (Bi) can be recoveredfrom the data. Additionally, from lemmas A.1-A.3, all locations with zero residential employment have zeroadjusted residential amenities.

We choose units in which to measure adjusted residential amenities such that the geometric mean of

adjusted residential amenities is equal to one: Bi =[∏S

i=1 Bi

] 1S

= 1, where a bar above a variable denotes ageometric mean. Therefore, dividing through by the geometric means in (45), adjusted residential amenitiescan be determined from:

Bi

Bi

=

(HRi

HRi

) 1ε(Qi

Qi

)1−β (Wi

W i

)− 1ε

. (47)

A.3.1.3 Final Goods Productivity

Given the parameters α, µ, ε, κ, observed data Q,HM ,HR, τ and the above solutions for adjustedwages w, prot maximization and zero prots (24) determine a unique vector for adjusted productivity(A) up to the normalization chosen for adjusted wages. For all locations with positive workplace employ-ment, we require:

qj = (1− α)

(α

wj

) α1−α

A1

1−αj . (48)

Qj = (1− α)

(α

wj

) α1−α

A1

1−αj .

where qj denotes the price of commercial oor space and Qi denotes the observed price of oor space.For locations s ∈ =M ∪=S with positive workplace employment, commercial oor prices are related to

observed oor prices through qs = Qs. Adjusted nal goods productivity (A1

1−αj = E

αε(1−α)j A

11−αj ) captures

(i) nal goods productivity (Aj) in an employment location and (ii) the Fréchet scale parameter that deter-mines the average utility (or eective units of labor) for commuters to that location (Ej). Note that E

αε(1−α)j

enters the zero-prot condition isomorphically to A1

1−αj . Therefore only the composite adjusted nal goods

productivity (Aj) can be recovered from the data. Additionally, from lemmas A.1-A.3, all locations withzero workplace employment have zero adjusted nal goods productivity.

Lemma A.8 Given the parameters α, µ, ε, κ, observed data Q,HM ,HR, τ and the solution for adjustedwages w∗, there exists a unique vector of adjusted nal goods productivities A∗ ∈ RS

+ such that the zeroprot condition (48) holds for all locations with positive workplace employment.

Proof. The lemma follows immediately from the zero-prot condition (48).

26

A.3.1.4 Land Market Clearing

Given the parameters α, β, µ, ε, κ, the observed data Q,HM ,HR,K, τ and the above solutions for ad-justed wages and nal goods productivity w, A, the land market clearing condition determines a uniquevector for the adjusted density of development (ϕ).

For all locations with positive workplace employment, we can solve for adjusted commercial oor spaceuse from commercial land market clearing (30):

LMi =

(wiαAi

) 11−α

HMi, (49)

LMi =

(wi

αAi

) 11−α

HMi,

where adjusted commercial land use satises LMi = E1/εi LMi. From lemmas A.1-A.3, all locations with

zero workplace employment have zero adjusted commercial oor space use (LMi = LMi = 0).For all locations with positive residence employment, we can solve for adjusted residential oor space

use from residential land market clearing (29):

LRi = (1− β)

S∑s=1

(E

1/εs ws/dis

)ε∑S

r=1

(E

1/εr wr/dir

)εws HRi

Qi

, (50)

LRi = (1− β)

[S∑s=1

(ws/dis)ε∑S

r=1 (wr/dir)εws

]HRi

Qi

,

where Qi denotes the price of residential oor space and Qi denotes the observed price of oor space.Adjusted residential oor space use is dened as:

LRi = LRiζRi

∑Rs=1

(ws/dis)ε∑S

r=1(wr/dir)ε ws∑R

s=1(ws/dis)

ε∑Sr=1(wr/dir)

εws

E1/εs

. (51)

The parameter ζRi allows for land use regulations that introduce a wedge between commercial and resi-dential oor prices (ξi), where we allow this wedge (ξi) to vary across blocks. The fraction in (51) controlsfor the dierence between adjusted wages (wi = E

1/εi wi) and actual wages (wi). From lemmas A.1-A.3, all

locations with zero residence employment have zero adjusted residential oor space use (LRi = LRi = 0).Combining these solutions for adjusted commercial and residential oor space use, we can solve for the

adjusted density of development (ϕi) from land market clearing:

Li = LMi + LRi = ϕiK1−µi , (52)

where the adjusted density of development (ϕi) relates adjusted oor space (Li) to observed geographicalland area (Ki).

Lemma A.9 Given the parameters α, β, µ, ε, κ, observed data Q, HM , HR, K , τ and the solutions foradjusted wages and nal goods productivity w∗, A∗, there exists a unique vector of the adjusted density ofdevelopment ϕ∗ ∈ RS

+ such that the land market clearing condition (52) holds for all locations.

27

Proof. The lemma follows immediately from the land market clearing condition (52) together with com-mercial land market clearing (49) and residential land market clearing (50).

From commercial land market clearing (49) and residential land market clearing (50), we can also solvefor the fractions of adjusted oor space (L) allocated to commercial use (θi) and residential use (1− θi):

θi =

1 if HMi > 0 and HRi = 0,

LMi

LMi+LRiif HMi > 0 and HRi > 0,

0 if HMi = 0 and HRi > 0.

(53)

A.3.1.5 Utility, Amenities and Productivity

To abstract from changes in currency units over time, we divide observed oor prices in each year by theirgeometric mean for that year. Therefore observed oor prices (Q) are normalized to have a geometricmean of one in each year. Furthermore, as discussed above, we also normalize adjusted wages (w) andadjusted residential amenities (B) to each have a geometric mean of one in each year. We now discuss theimplications of these normalizations for the choice of units in which variables are measured.

First, the normalizations of observed oor prices and adjusted wages involve a choice of units in whichto measure adjusted nal goods productivity (A), as can be seen from the zero prot condition (48). Second,the normalizations of observed land prices, adjusted wages and adjusted residential amenities also imply achoice of units in which to measure utility. This can be seen from the population mobility condition, whichimplies that the reservation level of utility in the wider economy (U ) satises:

γ

[S∑r=1

S∑s=1

TrEs(drsQ

1−βr

)−ε(Brws)

ε

]1/ε

= U , (54)

γ

[S∑r=1

S∑s=1

(drsQ1−β

r

)−ε (Brws

)ε]1/ε

= U ,

where γ = Γ(ε−1ε

); Γ(·) is the Gamma function; and we have used wi = E

1/εi wi and Bi = BiT

1/εi ζ1−β

Ri .Third, the choice of units in which to measure oor prices, adjusted wages and adjusted nal goods pro-ductivity in turn implies a choice of units in which to measure the adjusted density of development (ϕ),as can be seen from commercial land market clearing (49), residential land market clearing (50) and overallland market clearing (52).

We make these normalizations for each year separately. But we recognize that the absolute levels ofadjusted amenities (B), adjusted nal goods productivity (A), the adjusted density of development (ϕ), andthe reservation level of utility in the wider economy (U ) could change over time (and in particular couldchange before and after division or reunication). Therefore the moment conditions in our estimation usea “dierence-in-dierence,” where the rst dierence is before and after division (or reunication) and thesecond dierence is between dierent parts of West Berlin. These moment conditions only exploit relativechanges in oor prices and other variables between dierent parts of West Berlin. This use of relativechanges implies that our estimation results are invariant to the choice of units in which to measure oor

28

prices, wages, adjusted amenities, adjusted nal goods productivity, the adjusted density of developmentand utility. Similarly, this use of relative changes implies that our estimation results are unaected bychanges over time in the absolute levels of adjusted amenities, adjusted nal goods productivity, the adjusteddensity of development or the reservation level of utility in the wider economy.

A.3.1.6 One-to-One Mapping from α, β, µ, ε, κ and the Observed Data to A, B, ϕ

We now combine the results in the above lemmas to establish a one-to-one mapping from the parametersα, β, µ, ε, κ and the observed data Q,HM ,HR,K, τ to the unobserved values of adjusted nal goodsproductivity, residential amenities and the density of development A, B, ϕ for each location.

Proposition A.3 Given the model’s parameters α, β, µ, ε, κ and the observed data Q,HM ,HR,K, τ,there are unique vectors of adjusted nal goods productivity (A∗), residential amenities (B∗), and the densityof development (ϕ∗) that are consistent with the data being an equilibrium of the model.

Proof. The proposition follows immediately from lemmas A.6-A.9 above.

To interpret this identication result, note that in models with multiple equilibria, the mapping fromthe parameters and fundamentals to the endogenous variables is non-unique. In such models, the inversemapping from the endogenous variables and parameters to the fundamentals can be either unique or non-unique. In the context of our model, Proposition A.3 conditions on the parameters α, β, µ, ε, κ anda combination of observed endogenous variables Q, HM , HR and fundamentals K , τ , and uses theequilibrium conditions of the model to determine unique values of the location characteristics A, B, ϕ.This identication result hinges on the data available. In the absence of any one of the ve observed variables(oor prices, workplace employment, residence employment, land area and travel times), these unobservedadjusted fundamentals would be under-identied, and could not be determined without making furtherstructural assumptions.

The economics underlying this identication result is as follows. Given observed workplace and res-idence employment, and our measures of travel times, worker commuting probabilities can be used tosolve for unique adjusted wages consistent with commuting market clearing (19). Given adjusted wagesand observed oor prices, the rm cost function can be used to solve for the unique adjusted productivityconsistent with zero prots (24). Given adjusted wages, observed oor prices and residence employmentshares, worker utility maximization and population mobility can be used to solve for the unique adjustedamenities consistent with residential choice probabilities (15). Finally, given observed land area, the implieddemands for commercial and residential oor space can be used to solve for the unique adjusted density ofdevelopment consistent with market clearing for oor space (31).

These relationships for prot maximization, zero prots, utility maximization, population mobility andland market clearing hold irrespective of whether productivity, amenities and the density of developmentare exogenous or endogenous (since agents are atomistic and take the behavior of others as given). Thereforethey hold regardless of whether the model has a single equilibrium (as with exogenous location characteris-tics) or multiple equilibria (as is possible with endogenous location characteristics). These relationships also

29

hold irrespective of the relative importance of the two components of productivity and amenities (exter-nalities and fundamentals). Therefore the model has a recursive structure, in which the adjusted values ofoverall productivity, amenities and the density of development A, B, ϕ can be determined using the sub-set of the parameters α, β, µ, ε, κ and the observed data. In the next subsection, we examine how overalladjusted productivity and amenities A, B can be broken down into their two components of externalitiesΥi, Ωi and fundamentals ai, bi using the remaining parameters λ, δ, η, ρ.

A.3.2 Determining a, b from α, β, µ, ε, κ, λ, δ, η, ρ and the Observed Data

We now establish the one-to-one mapping from the full set of parameters α, β, µ, ε, κ, λ, δ, η, ρ and theobserved data Q,HR,HM ,K , τ to adjusted production and residential fundamentals a, b. This involvesdecomposing adjusted productivity and amenities A, B into their two components of externalities Υ, Ωand adjusted fundamentals a, b.

We have already established a one-to-one mapping from the subset of parameters α, β, µ, ε, κ and theobserved data to adjusted productivity A. From our specication of productivity (40), there is in turn aone-to-one mapping from adjusted productivity A and the parameters λ, δ to production externalitiesand adjusted production fundamentals Υ, a:

ai = AiΥ−λi , Υi =

[S∑s=1

e−δτisHMs

Ks

], (55)

ai = AiΥ−λi ,

where adjusted production fundamentals (ai = Eα/εi ai) captures (i) production fundamentals (ai) and (ii)

the Fréchet scale parameter that determines the average utility from commuting to an employment location(Ei). Note that Eα/ε

i enters adjusted production fundamentals isomorphically to ai. Therefore only thecomposite adjusted production fundamentals (ai) can be recovered from the data. Additionally, from lemmasA.1-A.5, all locations with zero workplace employment have zero adjusted productivity and hence zeroadjusted production fundamentals.

Lemma A.10 Given the parameters α, β, µ, ε, κ, λ, δ, η, ρ, the observed data Q, HM , HR, K , τ andthe solution for adjusted nal goods productivity A∗, there exists a unique vector of adjusted productionfundamentals a∗ ∈ RS

+.

Proof. The lemma follows immediately from productivity (55).

We have also already established a one-to-one mapping from the subset of parameters α, β, µ, ε, κand the observed data to adjusted amenities B. From our specication of amenities (41), there is in turn aone-to-one mapping from adjusted amenities B and the parameters η, ρ to residential externalities andadjusted residential fundamentals Ω, b:

bi = BiΩ−ηi , Ωi =

[S∑s=1

e−ρτisHRs

Ks

], (56)

bi = BiΩ−ηi ,

30

where adjusted residential fundamentals (bi = biT1/εi ζ1−β

Ri ) include (i) residential fundamentals (bi), (ii) theFréchet scale parameter that determines the average utility (or eective units of labor) for commuters fromlocation i (Ti), and (iii) the relationship between observed and residential oor prices (ζRi). As discussedabove, the parameter ζRi includes the eects of land use regulations that introduce a wedge between com-mercial and residential oor prices (ξi), where we allow this wedge (ξi) to vary across blocks. Note that T 1/ε

i

and ζ1−βRi enter adjusted residential fundamentals isomorphically to bi. Therefore only the composite value

of adjusted residential fundamentals (bi) can be recovered from the data. Additionally, from lemmas A.1-A.5, all locations with zero residential employment have zero adjusted amenities and hence zero adjustedresidential fundamentals.

Lemma A.11 Given the parameters α, β, µ, ε, κ, λ, δ, η, ρ, the observed data Q,HM ,HR,K , τ and thesolution for adjusted residential amenities B∗, there exists a unique vector of adjusted residential fundamentalsb∗ ∈ RS

+.

Proof. The lemma follows immediately from residential amenities (56).

Combining the above results, we are in a position to establish the following proposition.

Proposition A.4 Given the model’s parameters α, β, µ, ε, κ, λ, δ, η, ρ and the observed data Q,HM ,HR,K , τ , there are unique vectors of adjusted production fundamentals (a∗) and adjusted residential fundamentals(b∗) that are consistent with the data being an equilibrium of the model.

Proof. The proposition follows immediately from Proposition A.3 and lemmas A.10-A.11.

Therefore the earlier Proposition A.3 established a one-to-one mapping from the known parametersand the observed data to adjusted productivity (A), amenities (B), and the density of development (ϕ).Proposition A.4 goes further in establishing a one-to-one mapping from the known parameters and theobserved data to the two components of adjusted productivity and amenities: production and residentialexternalities Υ, Ω and adjusted production and residential fundamentals a, b. As for the earlier Propo-sition A.3, the results in Proposition A.4 hold regardless of whether the model has a single equilibrium ormultiple equilibria. Conditional on the parameters and the observed combination of endogenous variablesand fundamentals, the structural relationships of the model contain enough information to uniquely deter-mine adjusted production and residential fundamentals a, b, which correspond to structural residuals thatensure the model exactly replaces the observed data as an equilibrium.

In our structural estimation of the model in section A.5, we use Propositions A.3 and A.4 as an inputinto our generalized method of moments (GMM) estimation, in which we determine both the parametersand the unobserved adjusted fundamentals.

This completes our characterization of the one-to-one mapping from the known parameters α, β, µ, ε,κ, λ, δ, η, ρ and the observed data Q,HM ,HR,K , τ to the unobserved location characteristics a, b, ϕ.

31

A.4 Gravity, Productivity and Amenities

In this section, we take a rst step towards examining the extent to which the model can account quan-titatively for the observed variation in the data. In particular, we use the recursive structure of the modeldiscussed in subsection A.3 to recover overall productivity, amenities and the density of development justusing the model’s gravity equation predictions for commuting ows, without making assumptions aboutthe relative importance or functional form of production and residential externalities.

A.4.1 Gravity

From the commuting probabilities (14), one of the model’s key predictions is a semi-log gravity equationfor commuting ows from residence i to workplace j:

ln πij = −ντij + ϑi + ςj, (57)

where the residence xed eects (ϑi) capture residence characteristics Bi, Ti, Qi; the workplace xedeects (ςj) capture workplace characteristics wj , Ej; the denominator in (14) is a constant that is absorbedinto the xed eects; commuting costs are dij = eκτij ; and travel times τij are measured in minutes. Theparameter ν = εκ is the semi-elasticity of commuting ows with respect to travel times and is a combinationof the commuting cost parameter κ and the commuting heterogeneity parameter ε.

To provide empirical evidence on these gravity equation predictions, we use micro data on a repre-sentative survey of individual commuters in Berlin for 2008, which report district of residence, district ofworkplace and individual bilateral travel times in minutes for 7,948 commuters. We use these micro surveydata to compute the probability that a worker commutes between any of the 12 districts of Berlin in 2008,which yields 12 × 12 = 144 pairs of bilateral commuting probabilities.9 We observe positive commutingprobabilities for all bilateral district pairs, although some district pairs have a small number of commuters inthese micro survey data. While the model uses measures of bilateral travel times that we construct based onthe transport network, the micro survey data includes self-reported travel times for each commuter. There-fore we augment the gravity equation derived from the model (57) with a stochastic error that capturesmeasurement error in travel times:

lnπij = −ντij + ϑi + ςj + eij, (58)

where we assume that this measurement error is uncorrelated with self-reported travel times.The gravity equation (58) yields predictions for commuting probabilities between pairs of blocks, whereas

the commuting survey data reports commuting probabilities between pairs of districts. Taking means acrosspairs of blocks within pairs of districts in (58), we obtain the following district-level predictions:

lnπIJ = −ντIJ + ϑI + ςJ + eIJ , (59)9The districts reported in the micro survey data are post-2001 districts, as discussed in the paper.

32

whereln πIJ = 1

SI

1SJ

∑SIi=1

∑SJj=1 lnπij,

τIJ = 1SI

1SJ

∑SIi=1

∑SJj=1 τij,

ϑI = 1SI

∑SIi=1 ϑi,

ςJ = 1SJ

∑SJj=1 ςj,

eIJ = 1SI

1SJ

∑SIi=1

∑SJj=1 eij,

and where I denotes the district of residence; J denotes the district of workplace; SI is the number of blockswithin district I ; SJ is the number of blocks within district J ; ln πIJ is the average of the log commutingprobabilities (ln πij) between all pairs of blocks i and j within the pair of districts I and J ; τIJ is the averageself-reported travel time between all pairs of blocks i and j within the pair of districts I and J ; ϑI are districtof residence xed eects; ςJ are district of workplace xed eects; and eIJ is a stochastic error.

In the commuting survey data, we observe average self-reported travel times between a pair of districts(τIJ ) on the right-hand side of (59). But we cannot construct the average of the log commuting probabili-ties between pairs of blocks within a pair of districts (lnπIJ ) on the left-hand side of (59), because we donot observe bilateral commuting probabilities between pairs of blocks (πij). Instead, we observe bilateralcommuting probabilities between pairs of districts (πIJ ). Therefore we proxy the unobserved lnπIJ withthe observed ln πIJ and estimate the following district-level gravity equation:

ln πIJ = −ντIJ + ϑI + ςJ + eIJ . (60)

To interpret this approximation, note that the district and block commuting probabilities are related asfollows:

πIJ =HIJ

H=

SI∑i=1

SJ∑j=1

Hij

H=

SI∑i=1

SJ∑j=1

πij,

where HIJ is the measure of commuters from district I to J . Taking logs and subtracting lnSI and lnSJ

from both sides of this relationship, we have:

ln πIJ − lnSI − lnSJ = ln

[1

SI

1

SJ

(SI∑i=1

SJ∑j=1

πij

)].

Substituting for the observed ln πIJ in our district-level gravity equation (60), we obtain:

ln

[1

SI

1

SJ

SI∑i=1

SJ∑j=1

πij

]+ lnSI + lnSJ = −ντIJ + ϑI + ςJ + eIJ ,

which can be re-written as:

ln

[1

SI

1

SJ

SI∑i=1

SJ∑j=1

πij

]= −ντIJ + θI + σJ + eIJ . (61)

where we have absorbed the terms in lnSI and lnSJ into the xed eects on the right-hand side: θI =

ϑI − lnSI and σJ = ςJ − lnSJ .

33

Comparing (59) and (61), our approximation of the unobserved lnπIJ with the observed lnπIJ amountsto approximating the mean of the log block commuting probabilities with the log of the mean block com-muting probabilities. If the bilateral commuting probabilities were the same for all pairs of blocks within apair of districts (πij = πIJ = κ for all pairs of blocks i, j within the pair of districts I, J ), these two variableswould take the same value:

ln[

1SI

1SJ

∑SIi=1

∑SJj=1 πij

]= ln

[1SI

1SJ

∑SIi=1

∑SJj=1 κ

]= lnκ,

lnπIJ = 1SI

1SJ

∑SIi=1

∑SJj=1 [lnκ] = lnκ.

More generally, these two variables dier from one another, because of Jensen’s inequality. We provideevidence on the quantitative relevance of this dierence below, by calibrating the model and comparing theresults of estimating gravity equations at the block and district level using data generated from the model.

In particular, we assume parameter values (ν = εκ = 0.07) and solve the model’s commuting marketclearing condition (equation (26) in the paper) for unobserved transformed wages (ωit = w

1/εit ). Using

these solutions, we generate the model’s predictions for bilateral commuting ows between blocks, andaggregate these ows between blocks to generate the model’s predictions for bilateral commuting owsbetween districts.

In this calibration, the gravity equation (57) holds exactly at the block-level with no stochastic error.Similarly, if we use the average of log commuting probabilities (ln πIJ ) between pairs of blocks withinpairs of districts, the gravity equation also holds exactly at the district-level. However, if we instead usethe log district commuting probabilities (lnπIJ ), the gravity equation does not hold exactly, because ofJensen’s inequality. Nonetheless, in practice, we nd that this discrepancy is small. Estimating the gravityequation using the log district commuting probabilities (ln πIJ ) from the model-generated data, we nd asemi-elasticity of ν = 0.0726 (close to the value of ν = 0.07 used to generate the data) and a regressionR-squared of 0.9888. Therefore we nd that estimates of the gravity equation at the district-level provide areasonable approximation to those at the block-level using data generated from the model.

A.5 Structural Estimation

We now turn to the structural estimation of the model, where both the parameters and the unobservedlocation characteristics are unknown and to be estimated. First, in subsection A.5.1, we use the resultsfrom section A.3 to express the unobserved production and residential fundamentals a, b as one-to-onefunctions of the observed data Q, HM , HR, K , τ and the parameters α, β, µ, ε, κ, λ, δ, η, ρ. Thereforethese unobserved location characteristics correspond to structural residuals of the model that are functionsof the observed data and parameters.

Second, in subsection A.5.2, we use the resulting closed-form solutions for these structural residuals toconstruct moment conditions using the exogenous variation provided by Berlin’s division and reunication.Third, in subsection A.5.3, we show how these moment conditions can be used to estimate the model’sparameters using the Generalized Method of Moments (GMM). Fourth, in subsection A.5.4 we discuss the

34

computationally demanding optimization problem over the parameter vector and the algorithms that weuse to solve this problem.

Fifth, in subsection A.5.5, we show how the moment conditions identify the parameters, and characterizethe properties of the GMM objective function in the parameter space. We show that the GMM objective hasa unique global minimum in the parameter space. We therefore nd that there is only a single parametervector that is consistent with the data under our identifying assumptions.

A.5.1 Structural Residuals

We rst use the results from section A.3 to write unobserved production and residential fundamentals asstructural residuals that are functions of the parameters and observed data. Of the model’s eight parameters,the share of residential oor space in consumer expenditure (1− β), the share of commercial oor space inrm costs (1− α), and the share of land in construction costs (1− µ) are hard to determine from our data,because information on consumer expenditures and factor payments at the block level is not available overour long historical sample period. As there is a degree of consensus about the value of these parameters,we set them equal to central estimates from the existing empirical literature. We set the share of residentialoor space in consumer expenditure (1 − β) equal to 0.25, which is consistent with the estimates in Davisand Ortalo-Magné (2011). We assume that the share of commercial oor space in rm costs (1 − α) is0.20, which is in line with the ndings of Valentinyi and Herrendorf (2008). We set the share of land inconstruction costs (1 − µ) equal to 0.25, which is consistent with the estimates in Combes, Duranton, andGobillon (2014) and Epple, Gordon, and Sieg (2010) and with micro data on property transactions for Berlinfrom 2000-2012.

Given these values for α, β, µ, we use the observed dataX = [Q HM HR K τ ] and the structure ofthe model to estimate the six parameters determining the strength of agglomeration forces and commutingcosts Λ = [ν ε λ δ η ρ]′ (where ν = εκ is the semi-elasticity of commuting ows with respect to traveltimes) and the unobserved characteristics for each location Φ =

[ϕ a b

]. From prot maximization and

zero prots (48) and productivity (55), the structural residual for adjusted production fundamentals can bewritten as the following function of the parameters and observed data:

ait

at=

(Qit

Qt

)1−α(wit

wt

)α(Υit

Υt

)−λ. (62)

where we now make time explicit with the subscript t and a bar above a variable denotes a geometric meanso that Qt = exp 1

S

∑Ss=1 lnQst; adjusted wages (wit) are a function of observed workplace employment,

residence employment and travel times HMit, HRit, τijt from commuting market clearing (42); productionexternalities (Υit) are a function of observed workplace employment, geographical land area and traveltimes HMit, Ki, τijt:

Υit =S∑s=1

e−δτistHMst

Ks

,

where in the estimation we exclude the own region i from the summation to rule out a mechanical corre-lation through own-region workplace employment.

35

From the residential choice probabilities (15), the expected utility from moving to the city (54) andamenities (56), the structural residual for adjusted residential fundamentals can be written as the followingfunction of the parameters and observed data:

bit

bt=

(HRit

HRt

) 1ε(Qit

Qt

)1−β (Wit

W t

)− 1ε(

Ωit

Ωt

)−η, (63)

where a bar above a variable again denotes a geometric mean. Adjusted commuting market access (Wit) isa function of adjusted wages (wit) and observed travel times (τijt):

Wit =

[S∑s=1

(wst/eκτist)ε

],

where adjusted wages (wit) are again a function of observed workplace employment, residence employmentand travel times HMit, HRit, τijt from commuting market clearing (42). Residential externalities (Ωit) area function of observed residence employment, geographical land area and travel times HRit, Ki, τijt:

Ωit =S∑s=1

e−ρτistHRst

Ks

,

where in the estimation we again exclude the own region i from the summation to rule out a mechanicalcorrelation through own-region residence employment.

We solve for these structural residuals for all of Berlin, both before the war and after reunication, andfor West Berlin during division. To structurally estimate the model’s parameters, we focus on the impactof division and reunication on West Berlin, since it remained a market economy and hence we expect themechanisms in the model to apply.10

We assume that each structural residual consists of a time-invariant xed eect (aFi , bFi and a time-varying stochastic shock (aVit , bVit . Taking dierences before and after division (or before and after reuni-cation), the xed eects are dierenced out, and we obtain the following expression for the relative changesin the structural residuals across blocks within West Berlin:

4 ln

(aVit

aV

t

)= (1− α)4 ln

(Qit

Qt

)+ α4 ln

(wit

wt

)− λ4 ln

(Υit

Υt

), (64)

4 ln

bVitbV

t

=1

ε4 ln

(HRit

HRt

)+ (1− β)4 ln

(Qit

Qt

)− 1

ε4 ln

(Wit

W t

)− η ln4

(Ωit

Ωt

), (65)

where a bar above a variable again denotes a geometric mean.The structural residuals in (64) and (65) correspond to double-dierenced adjusted production and res-

idential fundamentals. The rst dierence is before and after division (or before and after reunication)and is denoted by the time-dierence operator (4) in (64) and (65). This rst dierence eliminates any

10In contrast, the distribution of economic activity in East Berlin during division was heavily inuenced by central planning,which is unlikely to mimic market forces.

36

time-invariant factors with time-invariant eects, where we allow these xed eects to be correlated withthe endogenous variables of the model. The second dierence is across blocks within West Berlin and isreected in the normalization relative to the geometric mean in (64) and (65). This second dierence elimi-nates variables that are common across blocks within each time period (e.g. the reservation level of utility,Ut). It also ensures that our results are invariant to the choice of units in which to measure production andresidential fundamentals, since this choice of units is common across blocks and hence is dierenced out.

A.5.2 Moment Conditions

Our moment conditions exploit the exogenous change in the surrounding concentration of economic ac-tivity induced by Berlin’s division and reunication. Our identifying assumption is that double-dierencedlog adjusted production and residential fundamentals are uncorrelated with a set of indicator variables (Ikfor k ∈ 1, . . . , KI) capturing proximity to economic activity in East Berlin prior to division. Based on theresults of our reduced-form regressions, we measure proximity to economic activity in East Berlin usingdistance from the pre-war CBD, and use 50 indicator variables for percentiles of this distance distribution:

E[Ik ×4 ln

(ait/at

)]= 0, k ∈ 1, . . . , KI, (66)

E[Ik ×4 ln

(bit/bt

)]= 0, k ∈ 1, . . . , KI. (67)

This identifying assumption requires that the systematic change in the gradient of economic activity inWest Berlin relative to the pre-war CBD following division is explained by the mechanisms in the model(the changes in commuting access and production and residential externalities) rather than by systematicchanges in the pattern of structural residuals (production and residential fundamentals). Since Berlin’s divi-sion stemmed from military considerations during the Second World War and its reunication originated inthe wider collapse of Communism, the resulting changes in the surrounding concentration of economic ac-tivity are plausibly exogenous to changes in production and residential fundamentals in West Berlin blocks.

Since the moment conditions (66)-(67) are based on double dierences in adjusted production and res-idential fundamentals, they only exploit relative variation across dierent areas within West Berlin. Anychanges in the attractiveness of West Berlin relative to the larger economy that are common across locationswithin West Berlin are dierenced out. We do not use moment conditions in the adjusted density of devel-opment (ϕi) in our estimation, because the density of development could in principle respond to changesin the relative demand for oor space across locations within West Berlin as a result of the mechanisms inthe model (the changes in commuting access and production and residential externalities).

We augment these moment conditions for adjusted production and residential fundamentals with twoother moment conditions that use data on commuting travel times and wages for West Berlin during di-vision.11 The rst of these moment conditions requires that the total number of workers commuting for

11In the paper, we report over identication checks in which we show that the model using an estimated value of ν = εκ forone year is successful in capturing the pattern of commuting ows in other years of the data, suggesting that the commutingparameters are stable over our sample period.

37

less than 30 minutes in the model is equal to the corresponding number in the data. From the commutingmarket clearing condition (44), this moment condition can be expressed as:

E

ψHMjt −S∑

i∈ℵj

ωjt/eντijt∑S

s=1 ωst/eντijt

HRit

= 0, (68)

where ν = εκ; ψ is the fraction of workers that commute for less than 30 minutes in the data; ωit = wεit isa measure of transformed wages from solving the commuting market clearing condition (44); and ℵj is theset of residence locations i within 30 minutes travel time of workplace location j.

The second of these moment conditions requires that the variance of log adjusted wages (wit = ω1/εit ) in

the model is equal to the variance of log wages in the data (σ2lnwi

) for West Berlin during division:12

E[(1/ε)2 ln (ωjt)

2 − σ2lnwit

]= 0, (69)

where transformed wages (ωi) depend solely on ν, workplace employment, residence employment andtravel times from the labor market clearing condition (44); ε scales the variance of log adjusted wages (wi)relative to the variance of log transformed wages (ωi).

A.5.3 GMM Estimation

In this subsection, we briey review the Generalized Method of Moments (GMM) estimator (Hansen 1982,Cameron and Triveldi 2005) as applied to our setting.

One-Step GMM Estimator: Observations are indexed by i ∈ 1, . . ., N . The observed data are givenby the N × 5 vectorX = [Q HM HR K τ ]. There are M moment conditions and P parameters in theP × 1 vector Λ = [ν ε κ λ δ η ρ]′. Our moment conditions can be written as:

M (Λ) =1

N

N∑i=1

m(Xi,Λ) = 0, (70)

where m(Xi,Λ) is the moment function. The one-step GMM estimator solves:

ΛGMM = arg min

(1

N

N∑i=1

m(Xi,Λ)′

)W

(1

N

N∑i=1

m(Xi,Λ)

)(71)

where the weighting matrix W is the identity matrix. The estimated variance-covariance matrix for theone-step GMM estimates V (ΛGMM) is:

V(ΛGMM) =(G′WG

)−1 (G′WSW′G

)(G′WG

)−1

,

where G is the estimated M × P Jacobian of the M moment conditions with respect to the P parameters:

G =1

N

N∑i=1

∂m(Xi,Λ)

∂Λ′

∣∣∣∣∣ΛGMM

. (72)

12As reliable wage data for pre-war Berlin is unavailable, we use wages by workplace for West Berlin during division in ourmoment conditions, which is consistent with our use of the commuting data above.

38

The White (1980) heteroscedasticity robust estimator of the matrix S is:

S0 =1

N

N∑i=1

m(Xi, Λ)m(Xi, Λ)′.

To allow for spatial correlation of the structural errors, we report standard errors based on the Conley (1999)heteroscedasticity and autocorrelation consistent (HAC) estimator of the matrix S:

S = S0 +1

N

J∑j=1

ω(j)N∑

i=j+1

(m(Xi, Λ)m(Xi−j, Λ)′ +m(Xi−j, Λ)m(Xi, Λ)′

), (73)

which can be written as:

S = S0 +J∑j=1

$(j)(Sj + S′j

), (74)

where J is the maximum spatial lag between observations and$(j) is a spatial weight that is equal to one ifthe spatial distance is less than the specied maximum spatial lag and zero otherwise. We set the maximumspatial lag equal to 0.5 kilometers.

Two-Step (Ecient) GMM Estimator: The two-step (ecient) GMM estimator uses the ecient (opti-mal) weighting matrix (S−1) and solves:

ΛEGMM = arg min

(1

N

N∑i=1

m(Xi,Λ)′

)S−1

(1

N

N∑i=1

m(Xi,Λ)

),

where S is computed using the heteroscedasticity robust and autocorrelation consistent (HAC) estimator(73) evaluated at the one-step GMM parameter estimates (ΛGMM). The estimated variance-covariance matrixfor the two-step GMM estimates V (ΛE

GMM) is:

V(ΛEGMM) =

1

N

(G′S−1G

)−1

,

where G is computed using (72) evaluated at the ecient GMM parameter estimates (ΛEGMM); S is computed

using (73) evaluated at the ecient GMM parameter estimates (ΛEGMM).

A.5.4 Estimation Algorithms

The GMM estimator chooses the values of the model’s parameters Λ = [ν ε λ δ η ρ]′ to minimize the GMMobjective function (71). This optimization routine searches over alternative parameter vectors and evalu-ates the moment function m(Xi,Λ) for each parameter vector. Evaluating the moment function for eachparameter vector in turn involves solving a xed point problem for the transformed wage vector (ω) thatsolves the commuting market clearing condition (44). Solving this xed point problem is computationallydemanding, because it involves solving for transformed wages in 15, 937 blocks, where the matrix of com-muting probabilities includes 15, 937 × 15, 937 = 254 million bilateral commuting ows. We now discussthe algorithms that we use to solve these problems and estimate the model’s parameters.

39

We rst discuss the algorithm that we use to solve the xed point problem for transformed wages andhence evaluate the moment function m(Xi,Λ) for each parameter vector. We next discuss the algorithmsthat we use to search over alternative parameter vectors to minimize the GMM objective function.

Algorithms for evaluating the moment function for each parameter vector: To evaluate the mo-ment function for each parameter vector, we use the recursive structure of the model, as characterized inSection A.3 above:

1. Given ν and the observed data HR, HM , τ , the equilibrium transformed wage vector ω can beuniquely determined (up to a normalization) from the commuting market clearing condition (44) aloneindependently of the other equilibrium conditions of the model.

2. Given ν, ε, β, µ, the observed data Q, HR, HM , τ and solutions for transformed wages ω,adjusted amenities B can be uniquely determined (up to a normalization) from residential choices(47).

3. Given ν, ε, α, µ, the observed data Q, HR, HM , τ and solutions for transformed wages ω,adjusted productivity A can be uniquely determined from the zero prot condition (48).

4. Given ν, ε, α, β, µ, the observed data Q,HR,HM ,K , τ , and solutions for transformed wages andadjusted productivity ω, A, the adjusted density of development ϕ can be uniquely determinedfrom land market clearing (52).

5. Given ν, ε, α, β, µ, λ, δ, the observed data Q, HR, HM , K , τ , and solutions for adjusted produc-tivity A, adjusted production fundamentals a can be determined from the specication of produc-tivity (55)

6. Given ν, ε, α, β, µ, η, ρ, the observed data Q, HR, HM , K , τ , and solutions for adjusted residen-tial amenities B, adjusted residential fundamentals b can be determined from the specication ofresidential amenities (56)

We now consider these steps in turn.

1. The commuting market clearing condition (44) can be written as follows:

HM = C(ω)HR, (75)

where C(ω) is the matrix of commuting probabilities. Lemma A.3 establishes that locations withoutpositive workplace employment must have zero productivity and a zero wage. Furthermore, locationswith zero residence employment supply zero commuters to all workplace locations. Therefore, weset transformed wages equal to zero for all locations with zero workplace employment, and we setcommuting probabilities equal to zero for all source locations with zero residence employment andall destination locations with zero workplace employment. Hence, we can reduce the dimensionality

40

of the system of equations (75), such that HM is a NM × 1 vector, where NM is the number oflocations with positive workplace employment; HR is a NR × 1 vector, where NR in the number oflocations with positive residence employment; and C(ω) is a NM × NR matrix. Note that LemmasA.6-A.7 establish that the wage system (44) satises gross substitution and has a unique equilibrium.Therefore we solve for this unique equilibrium using the following iterative procedure. We guessan initial transformed wage vector ω0 and evaluate the matrix of commuting probabilities C(ω0)

to generate predicted workplace employment (HM ) given observed residence employment (HR).If predicted workplace employment is less than observed workplace employment for a location, weincrease our guess of the transformed wage for that location. If predicted workplace employment isgreater than observed workplace employment for a location, we decrease our guess of the transformedwage for that location. To update the transformed wage for a location, we compute an intelligent wageadjustment factor using the numerator of the commuting probabilities in (44): ω1 =

(HM/HM

)ω0.

We use this intelligent adjustment factor to update our guess of the transformed wage vector toω2 = (0.5 × ω1) + (0.5 × ω0). We then repeat the above process using this new guess for thetransformed wage vector ω2 until the wage system converges. Since the wage system (44) satisesgross substitution, this iterative procedure converges rapidly to the unique equilibrium transformedwage vector.

2. Solving for transformed wages is the only computationally-intensive component of the evaluation ofthe moment function m(Xi,Λ). Having solved for transformed wages ω, we can solve for adjustedamenities B, adjusted productivity A, the adjusted density of development ϕ, adjusted produc-tion fundamentals a, and adjusted residential fundamentals b from simple manipulations of singleequations in Steps 2-6 above, as shown in Propositions A.3 and A.4 in sections A.3.1 and A.3.2 of thisweb appendix respectively.

Algorithms for minimizing the GMM objective function with respect to the parameter vector:Having discussed our algorithms to evaluate the moment function for each parameter vector Λ = [ν ε λ δ η ρ]′,the algorithms for minimizing the GMM objective function with respect to the parameter vector are straight-forward. The estimation is undertaken in Matlab. To minimize the GMM objective function with re-spect to the parameter vector, we experimented with using both derivative-based constrained optimizationroutines (e.g. fmincon and the Knitro plug-in ktrlink for Matlab) and non-derivative-basedconstrained optimization methods (e.g. patternsearch and simulannealbnd from the GlobalOptimization Toolbox). To characterize the properties of the GMM objective in the parameterspace, we also undertook a grid search over the parameter space. As discussed in subsection A.5.5 below,the GMM objective is well-behaved in the parameter space. Therefore we obtain similar parameter estimatesfrom these alternative optimization routines and from alternative initial conditions. The results reported inthe paper are estimated using patternsearch.

41

Computational Time: Evaluating the moment function for a given parameter vector Λ = [ν ε λ δ η ρ]′,and hence solving for transformed wages for 15,937 blocks for this parameter vector, takes around 30 sec-onds of computing time on the latest generation of desktop computers. This process also uses a large amountof RAM to store the 15, 937 × 15, 937 = 254 million elements of the matrix of commuting probabilities.Minimizing the GMM objective function with respect to the parameter vector takes a few days on the latestgeneration of desktop computers. Therefore we trial code on a random sample of 25 percent of blocks onthe latest generation of desktop machines. This reduces the number of blocks for which we solve for trans-formed wages to 3,984 and hence reduces the size of the matrix of commuting probabilities to 1.59 millionelements. Once the code is up and running, we estimate the model for the full sample of blocks using thecomputer cluster of the Humboldt University of Berlin. Minimizing the GMM objective with respect to theparameter vector takes less than one day for the full sample using this computer cluster.

A.5.5 Identication

In Propositions A.3 and A.4, we show that we can use the equilibrium conditions of the model to exactlyidentify adjusted production and residential fundamentals ai, bi from the observed data Q, HM , HR,K , τ and known values of the model’s parameters ν, ε, λ, δ, η, ρ. Therefore adjusted production andresidential fundamentals are structural residuals that are one-to-one functions of the observed data andparameters, as demonstrated in subsection A.5.1. We now show how our moment conditions in termsof these structural residuals can be used to identify the model’s parameters (and hence recover both theunknown parameters and unobserved adjusted fundamentals).

An important feature of our GMM estimation is that we have closed-form solutions for the structuralresiduals of production and residential fundamentals in terms of the observed data and parameters. There-fore, when we consider alternative parameter vectors, we always condition on the same observed endoge-nous variables, and use Propositions A.3 and A.4 to solve for the implied values of production and residentialfundamentals. In contrast, in simulation methods such as simulated method of moments (SMM) or indi-rect inference, these closed-form solutions are typically not available. Hence these simulation methods arerequired to solve for alternative values of the endogenous variables for each parameter vector.

We identify the model’s parameters using moment conditions in terms of adjusted production and resi-dential fundamentals, commuting ows and wages, as discussed in subsection A.5.2. In principle, these mo-ment conditions need not uniquely identify the model’s parameters, because the objective function denedby them may not be globally concave. For example, the objective function could be at in the parameterspace or there could be multiple local minima corresponding to dierent combinations of the parametersν, ε, λ, δ, η, ρ and unobserved adjusted fundamentals a, b that are consistent with the same observeddata Q, HM , HR, K , τ . However, in practice, we nd that the objective function is well behaved inthe parameter space, and that our moment conditions determine a unique parameter vector. Below in thissubsection, we report the results of a grid search over the parameter space, in which we show that the GMMobjective has a unique global minimum that identies the parameters. In section A.7, we report the resultsof a Monte Carlo simulation, in which we generate data for a hypothetical city using known parameters,

42

and show that our estimation approach recovers the correct values of these known parameters.We now consider each of the moment conditions in turn and show how they identify the parameters

ν, ε, λ, δ, η, ρ. We begin with the semi-elasticity of commuting ows with respect to travel times (ν).A higher value of ν implies that commuting ows decline more rapidly with travel times, which impliesthat a larger fraction of workers commute for less than thirty minutes in the commuting moment condition(68). The recursive structure of the model implies that none of the other parameters ε, λ, δ, η, ρ aect thecommuting moment condition (ε only enters through ν = εκ and ωj). To characterize the properties of thecommuting moment condition in the parameter space, we undertake a grid search over 20 possible valuesof ν (from 0.01 to 0.20). In Figure A.3, we display the value of the commuting moment condition for WestBerlin for division for each value of ν. As apparent from the gure, the moment condition has a uniqueglobal minimum that identies ν.

We next consider the Fréchet shape parameter determining the heterogeneity of commuting decisions(ε). A higher value of ε implies a smaller dispersion in adjusted wages (wit) in the wage moment condition(69) for a given dispersion of transformed wages (ωit), since σ2

ln wit= (1/ε)2 σ2

lnωit. From the commuting

market clearing condition (44), transformed wages (ωit) depend solely on the parameter ν and observedworkplace employment, residence employment and travel times. The recursive structure of the model im-plies that none of the other parameters λ, δ, η, ρ aect the wage moment condition. To characterize theproperties of the wage dispersion moment condition in the parameter space, we undertake a grid searchover 20 possible values of ε (from 5 to 10) for our estimated value of ν. In Figure A.4, we display the valueof the wage dispersion moment condition for West Berlin during division for each value of ε. As shown inthe gure, the moment condition has a unique global minimum that identies ε.

We now turn to the parameters for production spillovers λ, δ and residential spillovers η, ρ. Althoughthe division of Berlin provides a single shock, we can separately identify these two sets of spillover param-eters. The reason is that adjusted productivity and amenities Ai, Bi can be separately recovered from theobserved data using the equilibrium conditions of the model (see (48) and (47)). Given these separate mea-sures of adjusted productivity and amenities, the productivity spillover parameters λ, δ could be estimatedfrom a regression of changes in productivity (Ai) on changes in production externalities (Υi), instrument-ing changes in production externalities with indicator variables for distance grid cells from the pre-warCBD. Similarly, the residential spillover parameters η, ρ could be estimated from a regression of changesin amenities (Bi) on changes in residential externalities (Ωi), instrumenting changes in residential exter-nalities with indicator variables for distance grid cells from the pre-war CBD. The exclusion restrictionsare that: (i) workplace employment aects adjusted productivity but not adjusted amenities, (ii) residenceemployment aects adjusted amenities but not adjusted productivities. Assumption (i) is the standard spec-ication of production externalities in urban economics and assumption (ii) models residential externalitiessymmetrically to production externalities, as discussed in subsection A.2.7. From the moment conditionsfor changes in production and residential fundamentals (66)-(67), our GMM estimator is similar to theseinstrumental variable regressions, but jointly estimates the parameters ν, ε, λ, δ, η, ρ as part of a systemthat includes our moment conditions for commuting and wages.

43

The division of Berlin implies a fall in production externalities (Υi) for the parts of West Berlin close tothe Berlin Wall. If this fall in production externalities does not fully explain the changes in adjusted pro-ductivity (Ait) close to the Berlin Wall, the remainder will be explained by a change in adjusted productionfundamentals (ait). The parameters λ, δ control the magnitude of the fall in production externalities andits rate of decay with travel time from Eastern concentrations of workplace employment. In Figure A.5,we show the mean changes in log adjusted production fundamentals following division across the distancegrid cells from the pre-war CBD used in the estimation for (i) the estimated parameters, (ii) for stronger ag-glomeration forces (larger λ and δ than estimated) and (iii) for weaker agglomeration forces (smaller λ andδ than estimated). From the moment condition (66), the production spillover parameters λ, δ are chosen tomake the mean changes in log adjusted production fundamentals (62) as at as possible across the distancegrid cells from the pre-war CBD.

To characterize the properties of the adjusted production fundamentals moment conditions in the pa-rameter space, we undertake a grid search over 20 possible values of λ (from 0.02 to 0.10) and 20 possiblevalues of δ (from 0.01 to 0.101) for our estimated values of ν and ε (400 parameter congurations). In FigureA.6, we display the sum of the squared mean changes in log adjusted production fundamentals across thedistance grid cells for our baseline specication pooling division and reunication. We construct contoursthrough this sum of squared mean changes in log adjusted production fundamentals for the 400 values ofλ, δ in the parameter space (shown on the horizontal and vertical axes). As shown in the gure, the sumof the squared mean changes in log adjusted production fundamentals has a unique global minimum in theparameter space that identies λ, δ.

Similarly, the division of Berlin implies a fall in residential externalities (Ωi) for the parts of West Berlinclose to the Berlin Wall. If this fall in residential externalities does not fully explain the changes in adjustedamenities (Bi) close to the Berlin Wall, the remainder will be explained by a change in adjusted residentialfundamentals (bi). The parameters η, ρ control the magnitude of the fall in residential externalities andits rate of decay with travel time from Eastern concentrations of residence employment. In Figure A.7,we show the mean changes in log adjusted residential fundamentals following division across the distancegrid cells from the pre-war CBD used in the estimation for (i) the estimated parameters, (ii) for strongeragglomeration forces (larger η and ρ than estimated) and (ii) for weaker agglomeration forces (smaller η andρ than estimated). From the moment condition (67), the residential spillover parameters η, ρ are chosen tomake the mean changes in log adjusted residential fundamentals (63) as at as possible across the distancegrid cells from the pre-war CBD.

To characterize the properties of the adjusted residential fundamentals moment conditions in the pa-rameter space, we undertake a grid search over 20 possible values of η (from 0.11 to 0.18) and 20 possiblevalues of ρ (from 0.31 to 1.01) for our estimated values of ν and ε (400 parameter congurations). In FigureA.8, we display the sum of the squared mean changes in log adjusted residential fundamentals for our base-line specication pooling division and reunication. We construct contours through this sum of squaredmean changes in log adjusted residential fundamentals for the 400 values of η, ρ in the parameter space(shown on the horizontal and vertical axes). As shown in the gure, the sum of the squared mean changes

44

in log adjusted residential fundamentals has a unique global minimum in the parameter space that identiesη, ρ.

A.6 Counterfactuals

Counterfactual Exercises: We consider three sets of counterfactual exercises. First, we simulate theimpact of division using the calibrated adjusted fundamentals from 1936. We capture division in the modelby assuming innite costs of trading the nal good, innite commuting costs (κ → ∞), innite rates ofdecay of production externalities (δ →∞), and innite rates of decay of residential externalities (ρ→∞)across the Berlin Wall. We choose the reservation level of utility in the wider economy following divisionto ensure that the total population of West Berlin (H) is equal to its value in the data in 1986.

Second, we simulate the impact of reunication using calibrated adjusted fundamentals for 1986 for WestBerlin and values of these fundamentals for either 2006 or 1936 for East Berlin. We capture reunication inthe model by assuming that the costs of trading the nal good across the Berlin Wall fall from innity to zeroand by assuming that commuting costs, the decay of production externalities and the decay of residentialexternalities across the Berlin Wall fall from innity to their estimated values. We choose the reservationlevel of utility in the wider economy following reunication to ensure that the total population of GreaterBerlin (H) is equal to its value in the data in 2006.

Third, we simulate the impact of changes in the matrix of bilateral travel times between locations (τ )as a result of a change in transport technology. In particular, we examine the impact of the automobile onthe location of economic activity within Berlin, by using the model to solve for the equilibrium distributionof economic activity in 2006 using travel time measures based solely on the public transport network. Tofocus on the impact of the change in transport technology in Berlin, we hold the reservation utility in thewider economy constant.

We undertake these counterfactuals for the special case of the model with exogenous productivity andamenities (λ = η = 0 and hence A = a and B = b) and for the estimated values of the agglomerationparameters λ, δ, η, ρ. We also examine counterfactual changes in the model’s agglomeration parametersλ, δ, η, ρ, including no production externalities (λ = 0), no residential externalities (η = 0) and half therates of spatial decay of production and residential externalities (δ, ρ half their estimated values).

In the special case of the model with exogenous productivity and amenities, there is a unique equilibrium(as shown in Proposition A.2 above). Therefore these counterfactuals yield determinate predictions for thespatial distribution of economic activity. In contrast, in the presence of agglomeration forces, there is thepotential for multiple equilibria in the model. We assume the equilibrium selection rule of solving for theclosest counterfactual equilibrium to the observed equilibrium prior to the counterfactual. In particular,we use the values of the endogenous variables from the observed equilibrium as our initial guess for thecounterfactual equilibrium. Using these initial values, we solve the model’s system of equations for a newvalue of the endogenous variables. We then update our guess for the counterfactual equilibrium based ona weighted average of these new values and the initial values. Finally, we repeat this process until thenew values and initial values converge. Our goal in these counterfactuals is not to determine the unique

45

impact on economic activity, but rather to examine whether the model with the estimated agglomerationparameters is capable of generating counterfactual treatment eects for division and reunication close tothe observed treatment eects.

Our structural estimation exactly explains the observed data, because we solve for unique values of thelocation fundamentals ai, bi, ϕi that replicate the observed data as an equilibrium of the model. In contrast,our counterfactuals assume alternative values for the location fundamentals and agglomeration parameters,and hence the model’s predictions are no longer necessarily equal to the observed data. We undertakecounterfactuals holding location fundamentals constant at their values before division or reunication toshow that the model can explain the observed treatment eects in the data through its agglomeration anddispersion forces rather than through changes in location fundamentals.

Exogenous Location Characteristics: To solve the counterfactuals with exogenous location character-istics, we use the following solution algorithm. We observe land area and travel times Ki, τij. We assumevalues for the model’s parameters α, β, µ, ν, ε and the adjusted location fundamentals ai, bi, ϕi, wherein this special case of the model Ai = ai and Bi = bi since λ = η = 0. We assume starting values for oorprices, adjusted wages and the fraction of adjusted oor space used commercially equal to their values inthe observed equilibrium prior to the counterfactual Q0

i , w0i , θ0

i . Given these starting values, we use theequilibrium conditions of the model to solve for new predicted values for these endogenous variables Q1

i ,w1i , θ1

i :

π1ij =

(dij (Q0

i )1−β)−ε (

Biw0j

)ε∑S

r=1

∑Ss=1

(drs (Q0

r)1−β)−ε (

Brw0s

)ε , (76)

π1ij|i =

(wj/dij)ε∑S

s=1 (ws/dis)ε

(77)

H1Ri =

S∑s=1

π1isH, (78)

H1Mi =

S∑r=1

π1riH, (79)

Y 1i = Ai

(H1Mi

)α (θ0i ϕiK

1−µi

)1−α, (80)

w1i =

αY 1i

H1Mi

, (81)

¯v1i = E

[w0s |i]

=S∑s=1

π1is|iw

0s , (82)

Q1i =

(1− α)Y 1i

θ0i ϕiK

1−µi

, i ∈ =M ∪ =S = Ai > 0, Bi = 0 ∪ Ai > 0, Bi > 0, (83)

Q1i =

(1− β)¯v1iH

1Ri(

1− θ0i

)ϕiK

1−µi

, i ∈ =R ∪ =S = Ai = 0, Bi > 0 ∪ Ai > 0, Bi > 0, (84)

46

θ1i = 1, i ∈ =M = Ai > 0, Bi = 0, (85)

θ1i = 0, i ∈ =R = Ai = 0, Bi > 0, (86)

θ1i =

(1− α)Y 1i

Q1i ϕiK

1−µi

, i ∈ =S = Ai > 0, Bi > 0. (87)

If the new predicted values for the endogenous variables of the model are equal to the starting values:

Q1i , w

1i , θ

1i = Q0

i , w0i , θ

0i ,

we have found the counterfactual equilibrium. If the new predicted values for the endogenous variables ofthe model are not equal to the starting values, we update the endogenous variables of the model using aweighted average of the starting values and the new predicted values:

Q2i = ςQ0

i + (1− ς)Q1i , (88)

w2i = ςw0

i + (1− ς)w1i ,

θ2i = ςθ0

i + (1− ς)θ1i ,

where 0 < ς < 1. We continue to solve the above system of equations for the equilibrium conditions of themodel until the endogenous variables converge to the counterfactual equilibrium.

As shown in Lemmas A.1-A.3, any location i ∈ =S = Ai > 0, Bi > 0 with strictly positive values ofboth productivity and amenities remains incompletely specialized; any location i ∈ =M = Ai > 0, Bi =

0 with strictly positive productivity and zero amenities remains completely specialized in commercialactivity; and any location i ∈ =R = Ai = 0, Bi > 0with zero productivity and strictly positive amenitiesremains completely specialized in residential activity. Furthermore, as shown in Proposition A.2, the generalequilibrium of the model with exogenous location characteristics is unique. Therefore, the above algorithmconverges rapidly to this unique equilibrium, and these counterfactuals yield determinate predictions forthe spatial distribution of economic activity.

EndogenousAgglomeration Forces: To solve the counterfactuals with endogenous agglomeration forces,we use a directly analogous solution algorithm. We observe land area and travel times Ki, τij. We assumevalues for the model’s parameters α, β, µ, ν, ε, λ, δ, η, ρ and the adjusted location fundamentals ai, bi,ϕi. We assume starting values for oor prices, adjusted wages and the fraction of adjusted oor spaceused commercially equal to their values in the observed equilibrium prior to the counterfactual Q0

i , w0i ,

θ0i . Given these starting values, we use the equilibrium conditions of the model to solve for new predicted

values for these endogenous variables Q1i , w1

i , θ1i . We expand the equilibrium conditions of the model

(76)-(87) to include the endogenous determination of adjusted productivity and amenities as a function ofproduction and residential externalities:

Υ1i =

S∑s=1

e−δτis(H1Ms

Ks

), (89)

A1i = ai

(Υ1i

)λ, (90)

47

Ω1i =

S∑s=1

e−ρτis(H1Rs

Ks

), (91)

B1i = bi

(Ω1i

)η. (92)

We continue to solve the system of equations for the equilibrium conditions of the model until the endoge-nous variables converge to the counterfactual equilibrium. As discussed above, in the presence of endoge-nous agglomeration forces, there is the potential for multiple equilibria in the model. Our use and updatingof the endogenous variables from the observed equilibrium as our initial guess for the counterfactual equi-librium implies that our equilibrium selection rule is to solve for the closest counterfactual equilibrium tothe observed equilibrium. Our goal in these counterfactuals is not to determine the unique impact of di-vision or reunication, but rather to examine whether the model with the estimated agglomeration anddispersion forces is capable of generating counterfactual treatment eects close to the observed data.

Transport Technology Counterfactual: Although the focus of our analysis is on the division and re-unication of Berlin, our quantitative model provides a tractable platform for undertaking a range of coun-terfactuals. As an illustration of the model’s potential, our nal counterfactual examines the impact of theautomobile on the location of economic activity within Berlin, by using the model to solve for the counter-factual equilibrium distribution of economic activity in 2006 using travel time measures based solely on thepublic transport network in 2006.

Our 2006 travel time measures using only public transport are typically higher than our baseline 2006measures that weight public transport and the automobile by their modal shares. Nevertheless the publictransport network is far more extensive in Berlin than in American cities (on average public transport,including walking and cycling, accounts for around two thirds of journeys in our 2006 data) and is relativelymore important for commuting into the central city. Table A.18 of this web appendix compares the actualand counterfactual travel times. As shown in rows 1-4 of the table, the unweighted average travel timeacross all possible bilateral connections with positive values of either workplace or residence employmentrises from 51 minutes to 70 minutes, and its standard deviation rises from 13 minutes to 26 minutes (sinceremote locations with high actual travel times and poor public transport connections are most aected). Asimplied by our gravity equation estimation in subsection 6.1 of the paper, commuting ows are higher onaverage for shorter travel times. Therefore, as shown in rows 5-6 of the table, if we weight travel times bythe actual bilateral commuting ows in the 2006 equilibrium, average travel times rise from 32 minutes to38 minutes.

The commuting technology facilitates a separation of workplace and residence, enabling people to workin relatively high productivity locations (typically in more central locations) and live in high amenity loca-tions (typically in suburban locations). The deterioration of the commuting technology triggers an outowof workers from Berlin, until oor prices fall such that expected utility in Berlin is again equal to the un-changed reservation level of utility in the wider economy. Total city employment and output fall by around14 and 12 percent respectively (rows 7-8 of the table). Output falls by less than employment, because laboris only one of the two factors of production and the total supply of oor space is held constant. On average

48

oor prices decline by 20 percent (row 9 of the table). This decline in oor prices is substantially larger forblocks experiencing above median increases in average unweighted travel times (typically in remote loca-tions) than for blocks experiencing below median increases in these travel times (typically in more centrallocations), as shown in rows 10-11 of the table.

The general equilibrium response of the economy to the deterioration in the commuting technologyis that locations become less specialized in workplace and residence activity, as shown in Figure A.9 ofthis web appendix. Panel A shows that blocks that are larger importers of commuters before the change intransport technology (larger net commuting on the horizontal axis) experience larger declines in workplaceemployment (on the vertical axis). Panel B shows that blocks that are larger exporters of commuters beforethe change in transport technology (smaller net commuting on the horizontal axis) experience larger de-clines in residence employment (on the vertical axis). A corollary of this decline in block specialization isa change in the pattern of worker sorting across bilateral pairs of workplace and residence locations. Eventhough travel times for a typical bilateral pair have increased, this change in worker sorting implies thataverage travel times weighted by commuting ows in the counterfactual equilibrium (row 12 of Table A.18)marginally decline relative to average travel times weighted by commuting ows in the actual equilibrium(row 5 of the table). Taken together, these results highlight that the model provides a framework that can beused to analyze the endogenous change in the organization of economic activity within cities in responseto changes in the transport network and other interventions (such as planning regulations).

A.7 Monte Carlo

As a further check on our identifying assumptions, we undertake a Monte Carlo exercise. We rst assumeparameter values and a data generating process for a hypothetical city. We next apply our estimationprocedure to the hypothetical city and show that it correctly recovers the assumed parameter values for thedata generating process.

In particular, we consider a hypothetical city on a 40× 40 latitude and longitude grid (1, 600 locations)of approximately the same dimensions as Berlin (ranging from latitude 52.4 to 52.6 and longitude 13.2 to13.4). We assume that each grid point has a land area of (K = 100) meters squared. We assume that traveltimes within the hypothetical city (τij) are proportional to the bilateral Great Circle distances between eachpair of locations (1, 600 × 1, 600 = 2, 560, 000 bilateral pairs). We assume the following expenditure andcost share parameters: α, β, µ=0.95, 0.90, 0.75. We assume the following values of the agglomerationand dispersion parameters: ν, ε, λ, δ, η, ρ=0.08, 4, 0.10, 0.08, 0.10, 0.08. We assume that the Fréchet scaleparameters for each residence location and employment location are equal to one (Ti = 1 and Ei = 1). Wealso assume that the tax equivalent of land use regulations is equal to one (ξi = 1).

We consider 50 replications of the model using realizations of random draws for production fundamen-tals, residential fundamentals and the density of development ai, bi, ϕi for each location on the latitudeand longitude grid. For each replication, we undertake the following procedure:

• Step 1: Using the assumed values for the model’s parameters α, β, µ, ν, ε, λ, δ, η, ρ and the realizations

49

of random draws for ai, bi, ϕi for each location on the latitude and longitude grid, we solve for theequilibrium of the hypothetical city before division.

• Step 2: We suppose that the hypothetical city is exogenously divided into Eastern and Western halves.We draw new realizations of the random draws for ai, bi, ϕi for each location on the latitude andlongitude grid in the Western half of the city.

• Step 3: We solve for the equilibrium of the Western half of the hypothetical city after division usingthese new realizations for ai, bi, ϕi.

• Step 4: We suppose that an econometrician observes only the same variables Qi,HMi,HRi,Ki, τij asin our data for Berlin before and after division, knows the parameters α, β, µ, and wants to estimatethe unknown parameters ν, ε, λ, δ, η, ρ and the location fundamentals ai, bi, ϕi.

• Step 5: We implement our estimation procedure. We calibrate the model to the observed equilibriumbefore division, calibrate the model to the observed equilibrium after division, compute our momentconditions and estimate the unknown parameters ν, ε, λ, δ, η, ρ using GMM.

• Step 6: We display the distribution of estimated parameters across the 50 replications and show thatwe correctly recover the true parameters ν, ε, λ, δ, η, ρ.

In Step 1, we draw realizations for production fundamentals, residential fundamentals and the density ofdevelopment ai, bi, ϕi for each location i on the latitude and longitude grid from an independent uniformdistribution on the interval [0.975, 1.025]. Given the assumed parameter values α, β, µ, ν, ε, λ, δ, η, ρ, therealizations ai, bi, ϕi and the other locational fundamentals Ti,Ei,Ki, ξi, τij, we solve for the equilibriumvalue of the endogenous variables of the model prior to division HMi, HRi, Qi, qi, wi, θi using the samesolution algorithm as used to undertake counterfactuals in subsection A.6. We use as starting values asymmetric distribution of the endogenous variables HMi, HRi, Qi, qi, wi, θi across all locations on thelatitude and longitude grid and hence solve for the closest equilibrium to this symmetric allocation.

In Step 2, we capture the division of the city into Eastern and Western halves by assuming innitecosts of trading the nal good, innite commuting costs (κ → ∞), innite rates of decay of productionexternalities (δ → ∞), and innite rates of decay of residential externalities (ρ → ∞) between the twohalves of the city. We draw new realizations for production fundamentals, residential fundamentals andthe density of development ai, bi, ϕi for each location i in the Western half of the city from the sameindependent uniform distribution.

In Step 3, we use the assumed parameter values α, β, µ, ν, ε, λ, δ, η, ρ, the new realizations ai, bi, ϕiand the other location characteristics Ti,Ei,Ki, ξi, τij to solve for the equilibrium value of the endogenousvariables of the model for the Western half of the city after division HMi, HRi, Qi, qi, wi, θi using the samesolution algorithm as used to undertake counterfactuals in subsection A.6. We use the initial values fromthe observed equilibrium prior to division as the starting values for the endogenous variables HMi, HRi,Qi, qi, wi, θi. Therefore we assume the equilibrium selection rule of solving for the closest equilibriumduring division to the observed equilibrium before division.

50

As discussed in section A.6 above, equilibrium total city population depends on the reservation level ofutility (U ) in the wider economy. Furthermore, our estimates of the model’s parameters and the treatmenteect of division are invariant with respect to U , because they are based on double dierences: relativecomparisons across locations within the Western half of the city before and after division. Therefore, wechoose U before division so that the total employment of the city prior to division is 3 million, and wechoose U after division so that the total employment of the Western half of the city is equal to its value atthe time of division.

In the GMM estimation in Steps 4-5, we use analogous moment conditions for the division of the hy-pothetical city as for the division of Berlin: the fraction of workers commuting less than a specied traveltime threshold, the dispersion of wages, and orthogonality conditions between the changes in productionand residential fundamentals and indicator variables for distance grid cells. We use ten indicator variablesbased on distance deciles.

In Panels A-F of Figure A.10, we display histograms of the estimated parameter values from each ofthe 50 replications, where the true value of each parameter is indicated by a vertical red line. To conservecomputational time in the Monte Carlo, we consider a much smaller number of locations in the hypotheticalcity (1,600) than in our actual data for Berlin (15,937). Nonetheless, we nd that the estimated parametervalues are closely centered around the true parameter values. Therefore, the results from this Monte Carloshow that, when the data are generated according to the model, our estimation procedure is successful inrecovering the correct values of the model’s parameters.

A.8 Introducing Non-traded Goods

In the baseline version of the model, we consider the canonical urban model with a single tradable nalgood and agglomeration economies in production and residential choices. A key focus of our analysis isthe extent to which this canonical urban model is able to account quantitatively and qualitatively for theobserved impact of division and reunication on the pattern of economic activity within West Berlin.

This note discusses two extensions of the model to introduce non-traded goods. The rst extensionallows for the consumption of non-traded goods at a worker’s place of work. The second extension allowsfor the consumption of non-traded goods at a worker’s place of residence. In principle, one can also considera hybrid specication, in which a constant fraction of worker’s expenditure on non-traded goods occurs attheir workplace and the remaining fraction occurs at their residence.

A.8.1 Non-Traded Goods by Workplace

In this section, we introduce non-traded goods that are consumed at a worker’s place of work. The con-sumption index for worker o residing at location i and working at location j is now:

Ci (cijo, `ijo) =Bizijodij

(cNijoβN

)βN (cT ijoβT

)βT ( `ijo1− βN − βT

)1−βN−βT, (93)

βN , βT > 0, 0 < βN + βT < 1,

51

where cNijo is consumption of the non-traded good at workplace location j; cT ijo is consumption of thetraded good; and commuting costs (dij) are modeled in terms of utility.

Utility maximization implies that total expenditure on the non-traded good for workers residing inlocation i and working in location j is a constant share of their income at their place of work:

pNjCNij = βNwjHMij, (94)

whereHMj is the total measure of workers (summing across the two sectors) that work in block j and residein block i.

The non-traded good is assumed to be produced under conditions of perfect competition and accordingto a constant returns to scale technology with a unit labor requirement:

YNj = HNj, (95)

where YNj is the measure of the non-traded good produced in location j and HNj is the measure of laboremployed in this production. For simplicity, we abstract from agglomeration economies in the productionof non-traded goods, although they also can be introduced. Perfect competition and constant returns toscale imply that the price of the non-traded good is equal to the wage:

pNj = wj. (96)

We now combine this result with utility maximization (94), aggregate across residence locations i for eachworkplace location j, and use goods market clearing for the non-traded good for each workplace locationj (∑

iCNij = CNj = YNj):YNj = βNHMj. (97)

Combining this result with the production technology (95), employment in producing non-traded goods ineach workplace location is a constant share of total employment in that workplace location:

HNj = βNHMj, (98)

while the remaining share of total employment is allocated to producing traded goods (HTj):

HTj = (1− βN)HMj. (99)

The model remains the same as in our baseline specication. The labor market clearing condition againdetermines wages in location j as a function of total workplace employment in that location and residenceemployment in all locations. The only dierence is that only a fraction of workplace employment is allocatedto the traded sector, with the remaining fraction allocated to the non-traded sector.

A.8.2 Non-Traded Goods by Residence

In this section, we introduce non-traded goods that are consumed at a worker’s place of residence. Theconsumption index for worker o residing at location i and working at location j is again (93), except thatnon-traded goods are now consumed at the worker’s residence i.

52

Utility maximization implies that total expenditure on the non-traded good for workers residing inlocation i is a constant share of their income at their place of residence:

pNiCNi = βNE [ws|i]HRi, (100)

where HRi is the total measure of residents of block i.The non-traded good is assumed to be produced under conditions of perfect competition and according

to a constant returns to scale technology with a unit labor requirement:

YNi = HNi, (101)

where YNi is the measure of the non-traded good produced in location i and HNi is the measure of work-ers employed in that production. For simplicity, we again abstract from agglomeration economies in theproduction of non-traded goods, although they also can be introduced. Perfect competition and constantreturns to scale imply that the price of the non-traded good is equal to the wage:

pNi = wi. (102)

Combining this result with utility maximization (100) and using goods market clearing for the non-tradedgood for each residence location i (CNi = YNi) and the production technology (101), we have:

HNi = βNE [ws|i]HRi

wi. (103)

Therefore employment in non-traded production is a function of the total measure of residents and the ratioof expected worker income to wages. The model remains as in our baseline specication. The labor marketclearing condition again determines wages in location i as a function of total workplace employment inthat location and residence employment in all locations. Employment in the traded sector follows fromtotal workplace employment minus employment in the non-traded sector.

A.9 Additional Reduced-Form Empirical Results

In this section, we report additional reduced-form results discussed in Section 5 of the paper.

A.9.1 Maps of Changes in Floor Prices

In Figures A.1-A.2 of the web appendix (discussed in subsection 5.1 of the paper), we provide further ev-idence on the impact of division and reunication by displaying the log dierence in land prices from1936-1986 and 1986-2006 for each block. As evident from the gures, the largest declines in land pricesfollowing division and the largest increases in land prices following reunication are along those segmentsof the Berlin Wall around the pre-war CBD. In contrast, there is little evidence of comparable declines inland prices along other sections of the Berlin Wall. Therefore these results suggest that it is not proximityto the Berlin Wall per se that matters but rather the loss of access to the pre-war CBD.

53

Comparing Figures A.1-A.2, it is striking the extent to which the areas that experienced the largestdecreases from 1936-1986 are also the areas that experienced the largest increases from 1986-2006. Re-gressing the growth in oor prices from 1986-2006 on the growth in oor prices from 1936-1986, we ndan estimated coecient (Conley standard error) of -0.262 (0.017) and an R-squared of 0.29. Estimating ananalogous regression for the ranks of the two growth rates, we nd a similar pattern of results, with anestimated coecient (Conley standard error) of -0.527 (0.019) and an R-squared of 0.28. Given that these arecross-section univariate regressions in growth rates using micro data, the strength of these relationships isstriking.

A.9.2 Baseline Dierence-in-Dierence Specication

Table A.1 reports a robustness test for division using standard errors clustered by statistical area (“Gebiet”)and demonstrates a similar pattern of results as in Table 1 in subsection 5.2 of the paper. Table A.2 reports thecoecients and standard errors on the other distance grid cells from Table 1 in the paper (omitted from thepaper to conserve space) using Heteroscedasticity and Autocorrelation Consistent (HAC) standard errorsfollowing Conley (1999).

Table A.3 reports a robustness test for reunication using standard errors clustered by statistical area(“Gebiet”) and demonstrates a similar pattern of results for division as in Table 2 in subsection 5.2 of thepaper. Table A.4 reports the coecients and standard errors on the other distance grid cells from Table2 in the paper (omitted from the paper to conserve space) using Heteroscedasticity and AutocorrelationConsistent (HAC) standard errors following Conley (1999).

A.9.3 Further Reduced-Form Evidence

Timing and Placebos Table A.5 re-estimates the “dierence-in-dierence” specication for division inTable 1 in the paper for the early-division period 1936-66 (discussed in subsection 5.3 of the paper). We reportHeteroscedasticity and Autocorrelation Consistent (HAC) standard errors following Conley (1999). TableA.6 reports the results of a robustness test using standard errors clustered on statistical areas (“Gebiete”).

Table A.7 re-estimates the “dierence-in-dierence” specication for division in Table 1 in the paper forthe late-division period 1966-86 (discussed in subsection 5.3 of the paper). We report Heteroscedasticity andAutocorrelation Consistent (HAC) standard errors following Conley (1999). Table A.8 reports the results ofa robustness test using standard errors clustered on statistical areas (“Gebiete”).

Transport Access We provide further evidence that the estimated treatment eects for division and re-unication are capturing a loss of access to the surrounding concentration of economic activity using adierent source of variation in the data based on transport access. In particular, division substantially re-duced the extent of the U/S-Bahn network accessible from West Berlin by closing o links to East Berlinand East Germany, thereby reducing the transport access advantage from proximity to an U/S-Bahn sta-tion. That is, locations in West Berlin close to U/S-Bahn stations were more adversely aected by division,

54

because they lost access to locations in East Berlin to which they previously had low travel times. In con-trast, the eect on blocks in West Berlin further from U/S-Bahn stations was more muted, because they hadhigher travel times to East Berlin prior to division.

To provide evidence on such heterogeneous treatment eects of division and reunication, we constructan indicator variable for each block based on whether it lies within 250 meters from a U/S-Bahn station inthe 1936 transport network.13 Table A.9 reports the results of augmenting our regression specications fromTables 1 and 2 in the paper with this indicator variable. We report Heteroscedasticity and AutocorrelationConsistent (HAC) standard errors following Conley (1999). Table A.10 reports the results of a robustnesstest using standard errors clustered on statistical areas (“Gebiete”).

Following division, blocks close to a U/S-Bahn station experience a larger reduction in oor prices withineach distance cell, consistent with their greater transport access loss. In Column (1) of Table A.9, whichincludes only the distance grid cells and our U/S-Bahn indicator, we nd an estimated eect of around 13percent (since 1− e−0.143 = 0.13). These results are robust to controlling for district xed eects (Column(2)) and our full set of controls (Column (3)). Including our full set of controls in Column (3), we nd thatblocks close to a U/S-Bahn station experience around a 5 percent larger reduction in oor prices followingdivision.14

Following reunication, blocks close to a U/S-Bahn station experience a larger increase in oor priceswithin each distance grid cell, consistent with their greater transport access improvement. In Column (4),which includes only the distance grid cells and our U/S-Bahn indicator, we nd an estimated eect of around4 percent (since e0.037 − 1 = 0.04). These results are robust to controlling for district xed eects (Column(5)), although they become smaller in magnitude, and they loose statistical signicance once we include ourfull range of controls (Column (6)).

While proximity to a U/S-Bahn station provides a simple and transparent measure of transport access, wealso nd similar results using a measure of Eastern transport access loss based on the travel time weightedaverage of oor prices in East Berlin blocks, as reported in Ahlfeldt, Redding, Sturm, and Wolf (2012). Takentogether, these results provide further evidence that the treatment eects of division and reunication arecapturing a loss of access to the surrounding concentration of economic activity.

A.10 Additional Structural Estimates

A.10.1 Gravity, Productivity and Amenities

Table A.11 reports a robustness test using standard errors clustered by statistical area (“Gebiet”) and demon-strates a similar pattern of results as in Table 4 in subsection 6.2 of the paper.

13While we choose a threshold of 250 meters for proximity to a U/S-Bahn station because it divides blocks within the 500 meterdistance grid cells from the pre-war CBD into two roughly equal groups, we nd similar results using other distance thresholds.

14We experimented with including interactions between our U/S-Bahn indicator and the distance grid cells and nd that thecoecient on the U/S-Bahn indicator is relatively similar across distance grid cells. As reported in Ahlfeldt, Redding, Sturm, andWolf (2012), we nd similar results when we run separate locally-weighted linear squares regressions of the log dierence inoor prices on distance from the pre-war CBD for blocks within and beyond 250 meters from a U/S-Bahn station.

55

A.10.2 Structural Estimation

GMMModel Fit To provide evidence on the t of the estimated model, we examine the extent to whichthe changes in productivity and amenities at dierent distances from the pre-war CBD are explained bythe economic mechanisms in the model (changes in commuting access and production and residential ex-ternalities) rather than by the structural residuals (production and residential fundamentals). In particular,we solve for adjusted productivity and amenities, production and residential externalities, and adjustedproduction and residential fundamentals using our parameter estimates pooling division and reunicationfrom Table 5 in subsection 7.5 of the paper. We treat these solutions of the model as data and estimate ourreduced-form “dierence-in-dierence” specication (equation (22) in the paper). As shown in Table A.12,we nd substantial and statistically signicant treatment eects of division and reunication for overallproductivity and amenities Ai, Bi, which are similar in size to what we nd in our initial calibration ofthe model in subsection 6.2 of the paper. We also nd substantial and statistically signicant treatmenteects for production and residential externalities Υλ

i , Ωηi . In contrast, the estimated coecients on the

distance grid cells for production and residential fundamentals ai, bi are always small in magnitude andoften statistically insignicant. Our model therefore ts the moments that we are targeting (see (66) and(67)), which implies that the model can explain the changes in the organization of economic activity withinBerlin following division and reunication through its endogenous mechanisms of changes in commut-ing and production and residential externalities rather than through changes in fundamentals. Table A.13demonstrates a similar pattern of results using standard errors clustered by statistical area (“Gebiet”) insteadof Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors following Conley (1999).

GMMRobustness Test Our structural estimation in Table 5 in subsection 7.5 of the paper estimates boththe agglomeration and commuting parameters ν, ε, λ, δ, η, ρ. In Table A.14, we report a robustness testin which we constrain ν = εκ and ε to equal the values that we estimated in section 6.1 of the paper usingthe model’s gravity equation predictions for commuting ows. Using these values of ν = εκ = 0.07 andε = 6.83, we then structurally estimate the agglomeration parameters λ, δ, η, ρ using our moment con-ditions for production and residential fundamentals ((66) and (67) respectively). In Table A.14, we reportthe estimation results for division (Column (1)), reunication (Column (2)), and pooling division and reuni-cation (Column (3)). As apparent from the table, we nd similar estimated values of the agglomerationparameters λ, δ, η, ρ as in the baseline specication reported in Table 5 in subsection 7.5 of the paper.

GMM Overidentication Table A.15 reports the results of an overidentication test using the ratio ofoor space to land area discussed in subsection 7.7 of the paper. Table A.16 reports the results of an overi-dentication test using adjusted production and residential fundamentals ai, bi discussed in subsection 7.7of the paper.

GMM Counterfactuals Table A.17 reports a robustness test using standard errors clustered by statisti-cal area (“Gebiet”) and demonstrates a similar pattern of results as in Table 7 in subsection 7.8 of the paper.

56

Figure A.9 and Table A.18 report the results of the counterfactual for the change in transport technologydiscussed in subsection 7.8 of the paper. Figure A.9 shows the relationship between the counterfactualchanges in workplace and residence employment and net commuting (workplace minus residence employ-ment) in the initial equilibrium. Table A.18 examines the impact of the counterfactual change in transporttechnology on economic activity within Berlin.

A.11 Data Sources and Denitions

The data section of the main paper provides an overview of our various data sources. This appendix providesmore detail. Subsection A.11.1 discusses the construction of the data on employment by residence for thepre-war period. Subsection A.11.2 discusses the construction of the data on employment by workplace forthe pre-war period. Subsection A.11.3 discusses the construction of the travel times in minutes betweenblocks. Subsection A.11.4 discusses the construction of the data on other block characteristics. SubsectionA.11.5 discusses the commuting survey data. Subsection A.11.6 discusses the comparison of our standardland values data with micro data on property transactions.

A.11.1 Employment at Place of Residence 1930s

The 1933 census published data on population for each of the 20 pre-war districts of Berlin and also thepopulation of each street or segment of street in Berlin. We digitized the information on population bystreet and merged it to the modern block structure. In a rst step we used information on street namechanges provided on http://www.luise-berlin.de to convert the historical street names into the modernstreet names. In a second step we obtained a dataset from the Statistical Oce of Berlin (“Senatsverwaltungfür Berlin”) that contains information on the modern statistical blocks to which each street in Berlin iscontiguous. We use this information to distribute the population of each street equally across all blockswhich are contiguous with the street. In doing so we take into account whether blocks are water areasor parks to avoid population being allocated to these blocks. In the case of unmatched streets we correctmisspellings of street names in both datasets by using an algorithm that matches streets within the samedistrict and sub-district (“Ortsteil”) whose names only dier by one letter. In a small number of cases, weare unable to match a street to a block, in which case we spread the street’s population equally across allblocks within the same sub-district that have positive population. Finally, we convert our 1933 estimates ofpopulation in each of the modern blocks into employment by residence by using the labor force participationrates for each district (“Bezirk”) from the 1933 census.

A.11.2 Employment at workplace

To estimate the 1933 workplace employment in each modern block we take a two-step approach. In therst step we create estimates of 1933 private-sector employment in each modern block and in a second stepwe estimate 1933 public-sector employment in each block.

57

For the rst step we use two key data sources. First, the 1933 census published data on employment atworkplace in private enterprises in each district of Berlin (“Mitteilungen des Statistischen Amts der StadtBerlin” 1935). Data at a ner spatial scale was not published in pre-war censuses. Second, we obtained acopy of the 1931 company register of Berlin (“Handelsregister”). The company register contains the nameand registered address of each rm in Berlin and in 1931 lists just over 47,000 rms. We have enteredthe name and address of each of these rms. We use information on street name changes provided onhttp://www.luise-berlin.de to convert the historical addresses to their modern equivalent. The StatisticalOce of Berlin supplied us with a le that lists for each modern postal address in Berlin the block in whichthis address is located. We use this concordance to create a count variable which counts how many rmswere registered in each modern block in 1931. Due to incomplete or defective addresses, we managed toallocate 42,818 of the 47,098 rms listed in the company register to a modern block.

To spread total private-sector workplace employment across blocks within each district, we rst estimatethe relationship at the district level between log private-sector workplace employment from the 1933 censusand the log number of rms from the company register. In Figure A.11, we display the values for thesevariables for each district as well as the regression relationship between them. As apparent from the gure,we nd a close relationship between private-sector workplace employment and the number of rms at thedistrict level, with a regression R2 of over 0.75. We use the estimated coecients from this regression andthe number of rms in each block to construct a predicted share of that block in total district private-sectorworkplace employment. We then use these predicted employment shares to allocate the district totals acrossblocks within districts.

Since this rst step uses predicted employment shares to allocate district totals across blocks withindistricts, the district totals for private-sector workplace employment in our data are the same as in the 1933census. To further assess the reliability of predicting workplace employment at the block level using infor-mation on the number of rms, we use the 1987 census data for West Berlin, which reports both workplaceemployment and the number of establishments by block. In Figure A.12, we display log workplace employ-ment and the log number of establishments for all blocks with more than three workers and establishments(for condentiality reasons the disaggregated totals for blocks are only reported for observations with morethan three cases). As apparent from the gure, we also nd a close relationship between these two variablesat the block level, with a regression R2 of 0.57.

In the second step, we construct public-sector employment in 1933 for each modern block by combiningdata from the 1933 census with detailed information on the location of public buildings prior to the SecondWorld War. The occupational census of 1933 reports city-level totals of public sector employees and theirbreakdown into sub-categories such as civil servants in the federal and city administration, primary andsecondary school teachers, police ocers, or clergymen. To allocate these occupation-specic totals forBerlin across blocks, we used a detailed street map of Berlin showing the location of each public buildingprior to the Second World War and its purpose (e.g. federal government ministries, public utilities, schools).This map was compiled by the Allied occupation authorities in 1945 (War Oce 1945). We allocate the em-ployment of each occupational group (e.g. primary school teachers) across the buildings in which workers

58

from this group are typically employed (e.g. primary schools).

A.11.3 Travel Times Between Blocks in Berlin

To determine commuting costs in the model we need to know the minimum travel time between each ofthe 15,937 blocks of Berlin in our data, i.e. nearly 254 million (15,937×15,937) bilateral connections. Wehave computed these travel times for 1936, 1986 and 2006. In 1936, commuting to work by car was rare,and hence we construct minimum travel times using the public transport network.15 In 1986 and 2006, weconstruct minimum travel times by combining information on the public transport network and drivingtimes by car.

To construct minimum travel times between each pair of blocks i and j by public transport for thethree years, we collected information on the underground rail (“U-Bahn”), suburban rail (“S-Bahn”), tram(“Strassenbahn”) and bus (“Bus”) network of Berlin in each year. These networks were digitized usingArcGIS and we used the ArcGIS Network Analyst to compute the fastest connection between locations iand j. In this computation we allow passengers to combine all modes of public transport and walking tominimize the travel time between i and j. We use the following assumed travel speeds for each mode oftransport: 5km/h for walking, 25km/h for underground and suburban rail travel, 14.5km/h for trams and14.3km/h for buses. Whenever passengers change between modes of transport (e.g. changing from thesuburban rail to a bus) we assume that 3 minutes are lost in waiting time at each connection point. Thesespeeds of travel are taken from Vetter (1928). We assume that these speeds are the same in all three yearsof our dataset, which is supported by comparing these travel speeds to current public transport timetables.Note that these assumptions imply that the travel times from i to j and j to i are the same.

To construct minimum driving times by car between each pair of blocks i and j for 1986 and 2006,we obtained an ArcGIS shape le of the modern street network of Berlin from a commercial geographicaldata provider “Geofabrik” (www.geofabrik.de). This shape le contains information on the maximum andaverage speed on all streets in and around Berlin and also restrictions on driving such as one-way streetsor prohibited turns. Therefore, the driving times from i to j and from j to i do not have to be the same,because of one-way streets and other similar restrictions on road trac. Using the ArcGIS Network Analyst,we computed the minimum driving times between all pairs of locations i and j using the average travelspeed on each street. As a check on our ArcGIS calculations, we compared the resulting bilateral minimumdriving times for 100 randomly selected blocks to those computed using Google Maps.16

Figure A.13 shows a scatter plot of our ArcGIS travel times and the Google travel times for the 10,000bilateral connections between the 100 randomly chosen blocks. The correlation between the two estimatesof bilateral driving times within Berlin is nearly 0.94. Our estimates of the car travel times are slightlylower than Google’s, with the median dierence being 7.9 minutes. To compute the 1986 car travel times,we restricted the road network to streets in West Berlin. We also adjusted the shape le to account for the

15Leyden (1933) reports data on travel by mode of transport in pre-war Berlin, in which travel by car accounts for less than 10percent of all journeys.

16Under its public use license Google restricts users to a small number of requests for travel times per day. Using Google’spublic use license to compute all 254 million bilateral driving times would have taken several years.

59

small number of changes in the main road network of West Berlin between 1986 and 2006.17

To combine the minimum travel times by public transport and car in 1986 and 2006 into a single traveltime measure, we use data on the proportion of journeys undertaken by these two modes of transport inBerlin. In particular we use information on the modal split of commuting journeys in each of the 12 present-day districts of Berlin from Senatsverwaltung für Stadtentwicklung (2011). In this data the average shareof journeys by car is about one third. We use this data to estimate a simple logit regression that explainsthe share of journeys undertaken by car in each of the 12 modern districts as a function of the averagedierence in driving times by car and public transport between blocks in this district and any other blockin Berlin. In particular we estimate the following regression

ln

(card

1− card

)= β1 + β2∆d + εd (104)

where d indexes districts, card is the share of journeys undertaken by car and ∆d is the average dierencein travel times between public transport and driving over all bilateral block connections involving districtd. Figure A.14 displays the tted values from this regression against the actual values of the data.

Using the parameter estimates from this regression we predict the share of journeys undertaken by carfor each bilateral commute between two blocks in Berlin. Our nal estimate of the average travel timebetween two blocks i and j is the weighted average of the car and public transport travel times usingthe predicted car and public transport shares as weights. We use the same weights to combine the publictransport and car travel times for 1986.18

A.11.4 Block Characteristics

We have collected data on observable block characteristics from a number of sources, as discussed below.

Block Land Area and Centroids We used ArcGIS and a shapele provided by the Statistical Oce ofBerlin (“Senatsverwaltung”) to compute geographic land area in square meters and the centroid of eachblock for 2006. As discussed in the data section in the paper, we hold the 2006 block structure constant forall years in our data.

Distance to theNearestU-Bahn and S-Bahn station From each block centroid we compute the straight-line distance in meters to the nearest underground (U-Bahn) and suburban (S-Bahn) railway station in 1936,1986 and 2006. Shapeles showing the exact routing (line shapes) of the rail lines as well as the exact loca-tions of the stations (point shapes) in 2006 were provided by the Statistical Oce of Berlin (“Senatsverwal-tung”). We used historic network plans to identify those stations that did not exist in 1936 or 1986. Scansof historic network plans are available from the website of Berlin Verkehr (www.berliner-berkehr.de). Tocreate shapeles of the 1936 and 1986 networks we start from the 2006 shapeles and delete those parts

17The main changes to the urban motorway system between 1986 and 2006 include the extension of the A113 between Adler-shof and Kreuz Schönefeld, two small extensions of the A100 and the construction of the A111.

18We were unable to nd data on the modal split of commuting journeys in Berlin in 1986 by district. However, data in Kloas,Kuhfeld, and Kunert (1988) show that the overall share of journeys by car was very similar to 2006.

60

of the networks that did not exist in 1936 or 1986. In this backward adjustment process a small number ofstations were added that existed in 1936, but were no longer served in 2006 (and 1986).

Green Areas We used ArcGIS and a shapele provided by the Statistical Oce of Berlin (“Senatsverwal-tung”) to compute the straight-line distance in meters from each block centroid to the edge of the nearestgreen area (public parks, forests and other green public areas in 2005). We also compute the square metersof green area for each block.

Water Areas We used ArcGIS and a shapele provided by the Statistical Oce of Berlin (“Senatsverwal-tung”) to compute the straight-line distance in meters from each block centroid to the edge of the nearestcanal, river or lake. We also create a dummy variable for blocks that are adjacent to a canal, river or lake.

Schools We used ArcGIS and a shapele provided by the Statistical Oce of Berlin (“Senatsverwaltung”)to compute the straight-line distance in meters from each block centroid to the nearest school in 2006.

Noise To capture the average noise level within a block we used ArcGIS and data provided by the Statis-tical Oce of Berlin (“Senatsverwaltung”) on the (estimated) average noise levels expressed in decibels (db)for 10 × 10 meter grid cells. For each block, we compute the average noise level across the grid cells thatfall within the block.

Land Use The 2006 land value map published by the Committee of Valuation Experts (“Gutachterauss-chuss für Grundstückswerte”) denes zones (“Bodenrichtwertzonen”) that are homogenous in terms of landvalue, building density, and land use. We use this map to create four dummy variables for whether the typ-ical land use in a block is commercial, residential, industrial or mixed.

Second World War Destruction We constructed the share of the built-up area in a block that was de-stroyed during the Second World War as reported on a map from the Agency for Cartography of Berlin in1945 (“Gebäudeschäden im Gebiet der Stadt Berlin, Stand 1945, Topographische Karte 1:25000,” Herausge-ber: Hauptamt für Vermessung der Stadt Berlin).

Listed Buildings The number of listed buildings in a block in 2008 was created based on a shapeleprovided by the Statistical Oce of Berlin (“Senatsverwaltung”).

Urban Regeneration Policies Post-Reunication We constructed three dummy variables indicatingwhether a block belongs to a renewal area (“Sanierungsgebiet”) designated in 2002, a renewal area desig-nated in 2005, or an area of urban restructuring (“Stadtumbau West”) designated in 2005. Two shapelesshowing the exact boundaries of renewal areas and areas of urban restructuring were provided by the Sta-tistical Oce of Berlin (“Senatsverwaltung”).

61

Government Buildings Post-Reunication We construct a dummy variable for whether a major gov-ernment building was located in a block in 2006 using a map showing all government buildings in 2006provided by the Statistical Oce of Berlin (“Senatsverwaltung”).

Wages The Statistical Yearbook of Berlin reports mean wages for each district of West Berlin in 1986. Thedata refer to mean annual wages of blue collar workers working in the manufacturing industry.

A.11.5 Commuting Survey Data

Micro Commuting Survey Data 2008 Ahrens, Ließke, Wittwer, and Hubrich (2009) reports the resultsof a representative commuting survey in Berlin and several other large German cities for 2008. The surveyrecords for each trip that a respondent makes on the day of the survey the start and end district, timetravelled in minutes and purpose of the trip. In this data we observe for Berlin 7,984 journeys betweena worker’s place of residence and her place of work. We use these data to construct a matrix of bilateralcommuting probabilities between the 12 districts of Berlin in 2008.

We also use these data to construct the fractions of commuters with travel times in the following eightbins: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-75 and 75-90 minutes. In constructing the fractions ofcommuters for these travel time bins, we exclude the negligible fraction of workers that commute for longerthan 90 minutes (in one direction from residence to workplace), who are likely to be inuenced by factorsoutside the model. We therefore construct the fractions of commuters for these travel time bins conditionalon commuting for 90 minutes or less, so that the fractions add up to one.

Commuting Survey Data 1982 Brög (1982) reports the results of a representative commuting surveyof 27,560 households in West Berlin and West Germany. The data include 291 households in West Berlinand report travel times in minutes between place of residence and place of work. We use these data toconstruct the fraction of commuters with travel times in the following eight bins: 0-10, 10-20, 20-30, 30-40,40-50, 50-60, 60-75 and 75-90 minutes. We again exclude the negligible fraction of workers that commutefor longer than 90 minutes (in one direction from residence to workplace) and construct the commutingfractions conditional on commuting for 90 minutes or less so that they add up to one.

Commuting Survey Data 1930s The pre-war commuting data were taken from Feder (1939). In thesecond half of the 1930s, Gottfried Feder carried out a survey of commuting in Berlin. He surveyed a totalof 24,336 workers across eight work locations in Berlin that he intended to be representative for the city andwhich included industry, service and public sector employers. He asked respondents for the travel time inminutes from their place of residence to their place of work. We use these data to construct the fraction ofcommuters with travel times in the following six bins: 0-20, 20-30, 30-45, 45-60, 60-75 and 75-90 minutes. Weagain exclude the negligible fraction of workers that commute for longer than 90 minutes (in one directionfrom residence to workplace) and construct the commuting fractions conditional on commuting for 90minutes or less so that they add up to one.

62

A.11.6 Micro Data on Land Transactions

We follow the standard approach in the urban literature of assuming that oor space L is supplied by acompetitive construction sector that uses geographic land K and capital M as inputs. Following Combes,Duranton, and Gobillon (2014) and Epple, Gordon, and Sieg (2010), we assume that the production functiontakes the Cobb-Douglas form: Li = Mµ

i K1−µi . We now show that these assumptions are consistent with

the micro data on property transactions for Berlin from 2000-2012.From the rst-order condition for prot maximization in the construction sector, the ratio of capital to

land area depends on the price of land relative to the price of capital:

Mi

Ki

=µ

1− µRi

P, (105)

where Ri is the price of land and P is the common price of capital across all locations. From the zero-protcondition, total revenue from oor space equals total payments to capital and land:

QiLiKi

=PMi + RiKi

Ki

. (106)

Combining these two conditions, total oor space multiplied by the price of oor price and divided by landarea is a linear transformation of the price of land:

QiLiKi

=1

1− µRi. (107)

We have obtained access to condential data from the Committee of Valuation Experts, which containproperty transactions in Berlin from 2000-2012. In this data set we observe transaction prices, which corre-spond to QiLi, as well as the corresponding lot sizes, which correspond to Ki. We compare property pricesdivided by the lot size in these transactions data to the standard land values reported by the Committeethat are used in our empirical analysis. This comparison serves two purposes. First, a strong correlationwill indicate that the standard land values provided by the Committee are truly reective of the marketvaluation. Second, an approximately linear relationship will suggest that the Cobb Douglas functional formis a reasonable approximation for the construction sector in Berlin.

We adjust the observed prices in the property transactions data to 2006 prices using a Case-Shiller typerepeated sales approach at the block level. Unlike in conventional hedonic analysis of Qi there is no needto correct for housing attributes like the number of bathrooms or bedrooms because (QiLi)/Ki is directlyobserved in the data. However, since housing is durable and depreciates over time, it is important to controlfor the age of the building stock. We use the following specication to predict the average (log) price for anewly developed property per unit of geographic area (in meters squared) in a block in 2006 prices:

ln(Vkt) =∑m

bACm ADm +∑

n6=2006

bY Dn Y Dn + Φi + εkt. (108)

where k indexes properties; i indexes blocks and t indexes time; Vkt is the transaction price of a property ksold in year t divided by its lot size (land area);ADm is a full set of dummies for ten age cohortsm (0-5 years

63

is the base category); Y Dn is a full set of dummies for year n (2006 is the base category); εkt is a stochasticerror; and Φi is a time-invariant block specic xed eect, which we recover for further analysis.

The parameter estimates are reported in Table A.19. The transaction data set has sucient observa-tions to recover block xed eects for 8,907 blocks. Figure A.15 provides a comparison of this measure of(QiLi)/Ki to the 2006 land values assessed by the Committee of Valuation Experts, which correspond toRi. As predicted by our framework, the two measures are log-linearly related with a slope of approximatelyone. The transactions data we obtained also allows for a validation of the ratio of oor space to land area(GFZ) measure reported by the Committee. Figure A.16 compares the mean oor area divided by the lotsize for each block in the property transactions data to the values reported by the Committee. Again, wend that the two variables are closely correlated with a log slope of approximately one.

64

References

Ahlfeldt, G., S. Redding, D. Sturm, and N. Wolf (2012): “The Economics of Density: Evidence from theBerlin Wall,” CEP Discussion Paper, 1154.

Ahrens, G.-A., F. Liesske, R. Wittwer, and S. Hubrich (2009): “Endbericht zur Verkehrserhebung Mo-bilität in Städten - SrV 2008 und Auswertungen zum SrV-Städtepegel,” Dresden: Technische UniversitätDresden.

Albouy, D. (2008): “Are Big Cities Bad Places to Live? Estimating Quality of Life across Metropolitan Areas,”NBER Working Paper, 14472.

Alonso, W. (1964): Location and Land Use. Harvard, Cambridge MA.

American Embassy (1965): Handbook of Economic Statistics: Federal Republic of Germany andWestern Sectorsof Berlin. American Embassy, Bonn.

Brög, W. (1982): “Kontinuierliche Erhebung zum Verkehrsverhalten 1982 (KONTIV 82),” München: Institutfür Verkehrs- und Infrastrukturforschung.

Cameron, A. C., and P. K. Triveldi (2005): Microeconometrics: Methods and Applications. Cambridge Uni-versity Press, Cambridge.

Combes, P.-P., G. Duranton, and L. Gobillon (2014): “The Costs of Agglomeration: Land Prices in FrenchCities,” Wharton, mimeograph.

Conley, T. G. (1999): “GMM Estimation with Cross Sectional Dependence,” Journal of Econometrics, 92(1),1–45.

Davis, M. A., and F. Ortalo-Magné (2011): “Housing Expenditures, Wages, Rents,” Review of EconomicDynamics, 14(2), 248–261.

Duranton, G., andD. Puga (2004): “Micro-Foundations of Urban Agglomeration Economies,” in Handbookof Regional and Urban Economics, ed. by J. V. Henderson, and J.-F. Thisse, vol. 4, pp. 2063–2117. Elsevier,Amsterdam.

Eaton, J., and S. Kortum (2002): “Technology, Geography, and Trade,” Econometrica, 70(5), 1741–1779.

Epple, D., B. Gordon, and H. Sieg (2010): “A New Approach to Estimating the Production Function forHousing,” American Economic Review, 100(3), 905–924.

Feder, G. (1939): Arbeitstätte - Wohnstätte, Schriftenreihe der Reichsarbeitsgemeinschaft für Raum-forschung an der Technischen Hochschule Berlin. Julius Springer, Berlin.

Fujita, M., and H. Ogawa (1982): “Multiple Equilibria and Structural Transformation of Non-monocentricUrban Congurations,” Regional Science and Urban Economics, 12(2), 161–196.

65

Hansen, L. P. (1982): “Large Sample Properties of Generalized Method of Moments Estimators,” Economet-rica, 50(4), 1029–1054.

Kloas, J., H. Kuhfeld, and U. Kunert (1988): “Welche Entwicklung nimmt der Personenverkehr in Berlin-West? Zwei verkehrspolitische Szenarien,” Verkehr und Technik, 41(10), 383–395.

Leyden, F. (1933): Gross-Berlin: Geographie einer Weltstadt. Gebr. Mann Verlag, Berlin.

Lucas, R. E. (2000): “Externalities and Cities,” Review of Economic Dynamics, 4(2), 245–274.

McFadden, D. (1974): “The Measurement of Urban Travel Demand,” Journal of Public Economics, 3(4), 303–328.

Mills, E. S. (1967): “An Aggregative Model of Resource Allocation in a Metropolitan Centre,” AmericanEconomic Review, 57(2), 197–210.

Muth, R. (1969): Cities and Housing. University of Chicago Press, Chicago.

Roback, J. (1982): “Wages, Rents and the Quality of Life,” Journal of Political Economy, 90(6), 1257–1278.

Senatsverwaltung für Stadtentwicklung (2011): Stadtentwicklungsplan Verkehr. Senatsverwaltung,Berlin.

Sveikauskas, L. A. (1975): “The Productivity of Cities,” Quarterly Journal of Economics, 89(3), 393–413.

Valentinyi, A., and B. Herrendorf (2008): “Measuring Factor Income Shares at the Sectoral Level,” Reviewof Economic Dynamics, 11(4), 820–835.

Vetter, K. (1928): Ozieller Führer für Berlin und Umgebung und Potsdam und seine Schlösser. Rotophot,Berlin.

War Office (1945): Germany Town Plan of Berlin 1945, no. 4480 in Central Intelligence Unit and War Oce,Geographical Section. General Sta.

White, H. (1980): “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test forHeteroskedasticity,” Econometrica, 48(4), 817–838.

66

Figure A.1: Long-Dierenced Log Land Prices for Division (1936-86)

67

Figure A.2: Long-Dierenced Log Land Prices for Reunication (1986-2006)

68

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

1

2

3

4

5

6

7

8

9

10x 10

8

nu = kappa * epsilon

Com

mut

ing

Mom

ent

Figure A.3: Commuting Moment Condition (Sum of Squared Deviations)

69

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 100

0.5

1

1.5

2

2.5

3

3.5

4x 10

5

epsilon

Wag

e M

omen

t

Figure A.4: Wage Moment Condition (Sum of Squared Deviations)

70

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

4

6

8

10x 10

−3

Distance grid cell from pre−war CBD

Mea

n G

row

th P

rodu

ctio

n F

unda

men

tals

193

6−86

Weaker AgglomerationEstimated ParametersStronger Agglomeration

Figure A.5: Production Fundamentals Distance Grid Cell Moments (Division)

71

6.5e+04

6.63e+04

6.76e+04

6.9e+04

7.03e+04

7.17e+04

7.3e+04

7.43e+047.57e+04

6.36e+04

7.7e+04

7.84e+04

6.23e+04

7.97e+04

8.1e+04

6.09e+04

8.24e+04

8.37e+04

5.96e+04

8.5e+04

8.64e+04

8.77e+04

5.83e+04

8.91e+04

9.04e+045.69e+04

9.17e+04

9.31e+04

9.44e+04

9.58e+04

9.71e+04

7.57e+04

9.84e+04

9.98e+04

5.56e+04

7.7e+04

1.01e+05

1.02e+05

7.84e+04

1.04e+05

1.05e+05

7.97e+04

1.06e+05

8.1e+04

1.08e+05

8.24e+04

1.09e+05

8.37e+04

1.1e+05

5.43e+04

8.5e+04

1.12e+05

8.64e+04

1.13e+05

8.77e+04

8.91e+04

8.91e+04

1.14e+05

9.04e+04

9.17e+04

1.16e+05

9.31e+04

9.04e+04

9.44e+04

1.17e+05

9.58e+04

9.71e+04

9.84e+04

9.17e+04

1.19e+05

9.98e+04

1.01e+051.02e+05

1.2e+05

1.04e+05

9.31e+04

1.05e+051.06e+05

delta

lam

bda

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Figure A.6: Production Fundamentals Moment Condition (Sum of Squared Deviations)

72

0 5 10 15 20 25 30 35 40 45 50−4

−3

−2

−1

0

1

2

3

4

5x 10

−3

Distance grid cell from pre−war CBD

Mea

n G

row

th R

esid

entia

l Fun

dam

enta

ls 1

936−

86

Weaker AgglomerationEstimated ParametersStronger Agglomeration

Figure A.7: Residential Fundamentals Distance Grid Cell Moments (Division)

73

5.31e+04

5.37e+04

5.43e+04

5.49e+04

5.55e+04

5.6e+04

5.66e+04

5.78e+04

5.84e+04

5.9e+04

5.96e+04

6.01e+04

6.07e+04

6.13e+04

6.19e+04

6.25e+04

6.31e+04

6.36e+04

6.42e+04

6.48e+04

6.54e+04

6.6e+04

6.66e+04

6.72e+04

6.77e+04

6.83e+04

6.89e+04

5.25e+04

6.95e+04

7.01e+04

7.07e+04

7.13e+04

7.18e+04

7.24e+04

7.3e+04

7.36e+04

7.42e+04

7.01e+04

7.48e+04

7.07e+04

7.13e+04

7.54e+04

7.18e+04

7.59e+04

7.24e+04

7.65e+04

7.3e+04

7.71e+04

7.36e+045.78e+04

7.42e+04

7.77e+04

7.48e+04

7.83e+04

7.54e+04

7.89e+04

7.59e+045.84e+04

7.65e+04

7.95e+04

7.71e+04

8e+04

7.77e+04

8.06e+04

7.83e+047.89e+04

8.12e+04

5.9e+04

rho

eta

0.4 0.5 0.6 0.7 0.8 0.9 10.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

Figure A.8: Residential Fundamentals Moment Condition (Sum of Squared Deviations)

74

-400

0-3

000

-200

0-1

000

010

00C

ount

erfa

ctua

l-Act

ual W

orkp

lace

Em

ploy

men

t

-5000 0 5000 10000 15000Net Commuting (Workplace-Residence Employment)

Panel A: Workplace Employment

-600

-400

-200

020

0C

ount

erfa

ctua

l-Act

ual R

esid

ence

Em

ploy

men

t

-5000 0 5000 10000 15000Net Commuting (Workplace-Residence Employment)

Panel B: Residence Employment

Note: variables on horizontal and vertical axes normalized to have a mean of zero.

Figure A.9: Simulated Change in Workplace and Residence Employment

75

0 0.05 0.1 0.15 0.20

10

20

30

40

50Panel A : nu = epsilon * kappa

Fre

quen

cy

2 4 6 8 10 12 140

10

20

30

40

50Panel B : epsilon

Fre

quen

cy

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50Panel C : lambda

Fre

quen

cy

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50Panel D : delta

Fre

quen

cy

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50Panel D : eta

Fre

quen

cy

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50Panel E : rho

Fre

quen

cy

Note: Vertical red line indicates true parameter values.

Figure A.10: Monte Carlo Results (50 Replications)

76

CharlottenburgFriedrichshain

Kreuzberg

Kˆpenick

Lichtenberg

Mitte

Neukˆlln

Pankow

Prenzlauer Berg

Reinickendorf

SchˆnebergSpandau

SteglitzTempelhof

Tiergarten

Treptow

Wedding

Weiflensee

Wilmersdorf

Zehlendorf

910

1112

13D

istri

ct L

og E

mpl

oym

ent

5 6 7 8 9 10District Log Number of Firms

Note: the graph shows the correlation between the log number of firms in the 1931 companyregister in each district of Berlin and the log of total private-sector workplace employmentin the 1933 census. The R2 of the regression is 0.77.

Figure A.11: District Employment and Number of Firms

77

02

46

810

Log

wor

kpla

ce e

mpl

oym

ent

1 2 3 4 5 6Log number of establishments

Note: the graph shows the relationship between log workplace employment and the log numberof establishments across blocks in West Berlin (as reported in the 1987 census) and theregression relationship between them. The R2 of the regression is 0.57.

Figure A.12: Block Employment and Establishments 1987

78

010

2030

4050

60D

rivin

g Ti

me

Goo

gle

0 10 20 30 40 50 60Driving Time ArcGIS

Note: The graph shows bilateral travel times in minutes for 100 randomly selected blocks inBerlin. The travel time for these 10000 bilateral connections was computed using bothGoogle's public use license and the ArcGIS Network Analyst. The correlation betweenthese two measures of driving time is 0.94.

Figure A.13: ArcGIS Versus Google

79

Charlottenburg,Wilmersdorf

Friedrichshain,Kreuzberg

Mitte,Tiergarten,Wedding

Neukˆlln

Reinickendorf

Schˆneberg,Tempelhof

Spandau

Zehlendorf,Steglitz

.2.3

.4.5

.6

Shar

e of

car

s jo

urne

ys in

all

trips

30 40 50 60

Average travel time advantage of cars over public transport (min)

logit fit district

Note: the graph shows the results of a logit regression that relates the share of carjourneys in overall journeys in a district in 2010 to the average time saving from undertakinga trip originating in this district by car rather than public transport. See the main textfor data sources and details of the estimation.

Figure A.14: Car Journeys in Overall Trips

80

-4-2

02

4Ze

ro m

ean

adju

sted

200

6 lo

g (p

rice

/ lot

siz

e)

-2 0 2 4Zero mean 2006 log land value reported by Committee

Figure A.15: Transaction Price versus Assessed Value

Figure A.15: Transactions Prices Versus Assessed Value

81

-4-2

02

4Ze

ro m

ean

adju

sted

200

6 lo

g (p

rice

/ lot

siz

e)

-2 0 2 4Zero mean 2006 log land value reported by Committee

Figure A.15: Transaction Price versus Assessed Value

Figure A.16: Density of Development Versus Assessed GFZ

82

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Δ ln

QΔ

ln Q

Δ ln

QΔ

ln Q

Δ ln

QΔ

ln E

mpR

Δ ln

Em

pRΔ

ln E

mpW

Δ ln

Em

pW

CB

D 1

-0

.800

***

-0

.567

***

-0

.524

***

-0

.503

***

-0

.565

***

-1

.332

***

-0

.975

***

-0.6

91

-0.6

39*

(0.1

07)

(0.1

08)

(0.1

08)

(0.1

08)

(0.1

17)

(0.4

21)

(0.2

62)

(0.5

12)

(0.3

62)

CB

D 2

-0

.655

***

-0

.422

***

-0

.392

***

-0

.360

***

-0

.400

***

-0

.715

**-0

.361

-1.2

53**

*

-1.3

67**

*(0

.059

)(0

.069

)(0

.068

)(0

.062

)(0

.073

)(0

.273

)(0

.233

)(0

.332

)(0

.175

)C

BD

3

-0.5

43**

*

-0.3

06**

*

-0.2

94**

*

-0.2

58**

*

-0.2

47**

*

-0.9

11**

*-0

.460

*-0

.341

-0.4

71**

*(0

.050

)(0

.059

)(0

.060

)(0

.051

)(0

.062

)(0

.232

)(0

.245

)(0

.311

)(0

.167

)C

BD

4

-0.4

36**

*

-0.2

07**

*

-0.1

93**

*

-0.1

66**

*

-0.1

76**

* -

0.35

6**

-0.2

59

-0

.512

***

-0

.521

***

(0.0

34)

(0.0

43)

(0.0

46)

(0.0

41)

(0.0

36)

(0.1

52)

(0.1

96)

(0.1

71)

(0.1

31)

CB

D 5

-0

.353

***

-0

.139

***

-0

.123

***

-0

.098

***

-0

.100

***

-0.

301*

*-0

.143

-0.4

36**

*

-0.3

40**

*(0

.028

)(0

.030

)(0

.033

)(0

.032

)(0

.024

)(0

.151

)(0

.159

)(0

.166

)(0

.121

)C

BD

6

-0.2

91**

*

-0.1

25**

*

-0.0

94**

*

-0.0

77**

*

-0.0

90**

* -

0.36

0**

-0.1

35

-0.

280*

*-0

.142

(0

.035

)(0

.029

)(0

.026

)(0

.026

)(0

.024

)(0

.141

)(0

.119

)(0

.138

)(0

.126

)

Inne

r Bou

ndar

y 1-

6Ye

sYe

sYe

sYe

sYe

sO

uter

Bou

ndar

y 1-

6Ye

sYe

sYe

sYe

sYe

sK

udam

m 1

-6Ye

sYe

sYe

sYe

sB

lock

Cha

ract

eris

tics

Yes

Yes

Yes

Dis

trict

Fix

ed E

ffect

sYe

sYe

sYe

sYe

sYe

sYe

sYe

sYe

s

Obs

erva

tions

6260

6260

6260

6260

6260

5978

5978

2844

2844

R-s

quar

ed0.

260.

510.

630.

650.

710.

190.

430.

120.

33

Not

e: T

his t

able

repo

rts a

robu

stne

ss te

st fo

r Tab

le 1

in th

e pa

per u

sing

clu

ster

ed st

anda

rd e

rror

s. Q

den

otes

the

pric

e of

floo

r spa

ce. E

mpR

den

otes

em

ploy

men

t by

resi

denc

e.

EmpW

den

otes

em

ploy

men

t by

wor

kpla

ce. C

BD

1-C

BD

6 ar

e si

x 50

0m d

ista

nce

grid

cel

ls fo

r dis

tanc

e fr

om th

e pr

e-w

ar C

BD

. Inn

er B

ound

ary

1-6

are

six

500m

grid

cel

ls fo

r di

stan

ce to

the

Inne

r Bou

ndar

y be

twee

n Ea

st a

nd W

est B

erlin

. Out

er B

ound

ary

1-6

are

six

500m

grid

cel

ls fo

r dis

tanc

e to

the

oute

r bou

ndar

y be

twee

n W

est B

erlin

and

Eas

t G

erm

any.

Kud

amm

1-6

are

six

500m

grid

cel

ls fo

r dis

tanc

e to

Bre

itsch

eid

Plat

z on

the

Kur

fürs

tend

amm

. Blo

ck c

hara

cter

istic

s inc

lude

the

loga

rithm

of d

ista

nce

to sc

hool

s, pa

rks

and

wat

er, l

and

area

of t

he b

lock

, the

shar

e of

the

bloc

k's b

uilt-

up a

rea

dest

roye

d du

ring

the

Seco

nd W

orld

War

, ind

icat

ors f

or re

side

ntia

l, co

mm

erci

al a

nd in

dust

rial l

and

use,

and

in

dica

tors

for w

heth

er a

blo

ck in

clud

es a

gov

ernm

ent b

uild

ing

and

urba

n re

gene

ratio

n po

licie

s pos

t-reu

nific

atio

n. R

obus

t sta

ndar

d er

rors

in p

aren

thes

es a

djus

ted

for c

lust

erin

g by

st

atis

tical

are

a ("

Geb

iete

"). *

sign

ifica

nt a

t 10%

; **

sign

ifica

nt a

t 5%

; ***

sign

ifica

nt a

t 1%

.

Table A.1: Robustness Test for Baseline Division Results (1936-1986), Clustered Standard Errors

83

(3)

(4)

(5)

(7)

(9)

(4)

(5)

(7)

(9)

Δ ln

QΔ

ln Q

Δ ln

QΔ

ln E

mpR

Δ ln

Em

pWΔ

ln Q

Δ ln

QΔ

ln E

mpR

Δ ln

Em

pW

INN

1 -0

.041

*-0

.035

0.

006

-0.0

05

-0

.658

***

KU

1

-0.1

66**

*

-0.1

92**

*

-1.3

50**

*

0.7

46**

*(0

.024

)(0

.024

)(0

.021

)(0

.118

)(0

.164

)(0

.025

)(0

.024

)(0

.331

)(0

.251

)IN

N 2

-0.0

16

-0.0

09

0.01

2-0

.019

-0

.252

K

U 2

-0

.142

***

-0

.149

***

-0.1

84

0.

362*

*(0

.023

)(0

.023

)(0

.021

)(0

.094

)(0

.168

)(0

.028

)(0

.029

)(0

.148

)(0

.162

)IN

N 3

0.00

90.

017

0.02

8

-0.2

45**

*-0

.223

K

U 3

-

0.14

5***

-0

.148

***

-0.

200*

*-0

.042

(0

.020

)(0

.020

)(0

.018

)(0

.093

)(0

.145

)(0

.022

)(0

.022

)(0

.092

)(0

.141

)IN

N 4

-0.0

10

0.00

20.

007

-0.

148

-0.0

02

KU

4

-0.0

94**

*

-0.1

00**

*

-0.2

81**

*-0

.003

(0

.019

)(0

.019

)(0

.018

)(0

.093

)(0

.143

)(0

.014

)(0

.013

)(0

.093

)(0

.117

)IN

N 5

0.00

60.

025

0.0

29*

-0.0

550.

008

KU

5

-0.1

41**

*

-0.1

43**

*

-0.2

53**

*

0.27

2**

(0.0

17)

(0.0

17)

(0.0

16)

(0.0

99)

(0.1

50)

(0.0

18)

(0.0

17)

(0.0

98)

(0.1

27)

INN

6-0

.016

0.

009

0.

025*

*-0

.013

-0

.065

K

U 6

-0

.098

***

-0

.094

***

-0.

159*

*

0.3

60**

*(0

.014

)(0

.013

)(0

.012

)(0

.083

)(0

.128

)(0

.012

)(0

.013

)(0

.073

)(0

.104

)O

UT

1

0.1

87**

*

0.1

89**

*

0.1

50**

*

0.6

44**

*

-1.3

00**

*(0

.013

)(0

.013

)(0

.014

)(0

.111

)(0

.228

)O

UT

2

0.2

01**

*

0.2

04**

*

0.1

70**

*

0.7

80**

*

-0.5

30**

*(0

.012

)(0

.012

)(0

.012

)(0

.082

)(0

.197

)O

UT

3

0.2

29**

*

0.2

31**

*

0.2

02**

*

0.6

78**

*

-0.5

69**

*(0

.012

)(0

.012

)(0

.012

)(0

.078

)(0

.156

)O

UT

4

0.2

12**

*

0.2

13**

*

0.1

90**

*

0.4

17**

*-0

.218

(0

.011

)(0

.011

)(0

.011

)(0

.065

)(0

.137

)O

UT

5

0.1

67**

*

0.1

68**

*

0.1

48**

*

0.2

35**

*-0

.251

*(0

.012

)(0

.013

)(0

.011

)(0

.071

)(0

.129

)O

UT

6

0.1

17**

*

0.1

18**

*

0.1

09**

*

0.15

3* -

0.31

7**

(0.0

12)

(0.0

12)

(0.0

10)

(0.0

78)

(0.1

41)

Not

e: T

his t

able

repo

rts th

e co

effic

ient

s and

stan

dard

err

ors o

n th

e ad

ditio

nal d

ista

nce

grid

cel

ls in

Tab

le 1

in th

e pa

per.

Q d

enot

es th

e pr

ice

of fl

oor s

pace

. Em

pR d

enot

es

empl

oym

ent b

y re

side

nce.

Em

pW d

enot

es e

mpl

oym

ent b

y w

orkp

lace

. IN

N1-

INN

6 ar

e si

x 50

0m d

ista

nce

grid

cel

ls fo

r dis

tanc

e fr

om th

e in

ner b

ound

ary

betw

een

East

and

Wes

t B

erlin

. OU

T1-O

UT6

are

six

500m

grid

cel

ls fo

r dis

tanc

e to

the

Out

er B

ound

ary

betw

een

Wes

t Ber

lin a

nd E

ast G

erm

any.

KU

1-K

U6

are

six

500m

grid

cel

ls fo

r dis

tanc

e to

Bre

itsch

eid

Plat

z on

the

Kur

fürs

tend

amm

. Col

umn

num

bers

refe

r to

the

colu

mns

in T

able

1 in

the

pape

r. Se

e Ta

ble

1 in

the

pape

r for

furth

er d

etai

ls. H

eter

osce

dast

icity

and

Aut

ocor

rela

tion

Con

sist

ent (

HA

C) s

tand

ard

erro

rs in

par

enth

eses

(Con

ley

1999

). *

sign

ifica

nt a

t 10%

; **

sign

ifica

nt a

t 5%

; ***

sign

ifica

nt a

t 1%

.

Tabl

e A2:

Bas

elin

e D

ivis

ion

Res

ults

(193

6-19

86),

Oth

er C

oeff

icie

nts f

rom

Tab

le 1

, Con

ley

Stan

dard

Err

ors

Table A.2: Other Coecients from Baseline Division Results (1936-1986), Conley Standard Errors

84

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Δ ln

QΔ

ln Q

Δ ln

QΔ

ln Q

Δ ln

QΔ

ln E

mpR

Δ ln

Em

pRΔ

ln E

mpW

Δ ln

Em

pW

CB

D 1

0.

398*

*

0.4

08**

*

0.3

68**

*

0.3

69**

*

0.28

1**

1

.079

***

1

.025

***

1.

574*

* 1

.249

*(0

.154

)(0

.128

)(0

.119

)(0

.118

)(0

.121

)(0

.312

)(0

.313

)(0

.678

)(0

.734

)C

BD

2 0

.290

*

0.28

9**

0.

257*

*

0.25

8**

0.19

10.

589*

0.53

8

0.68

4**

0.45

7(0

.165

)(0

.136

)(0

.127

)(0

.126

)(0

.125

)(0

.352

)(0

.340

)(0

.330

)(0

.351

)C

BD

3

0.12

2**

0.

120*

*

0.11

0**

0.

115*

* 0

.063

*0.

340

0.3

05*

0.32

6*0.

158

(0.0

49)

(0.0

47)

(0.0

42)

(0.0

44)

(0.0

33)

(0.2

11)

(0.1

75)

(0.1

87)

(0.2

05)

CB

D 4

0.0

33*

0.03

10.

030

0.03

40.

017

0.11

00.

034

0.33

6*0.

261

(0.0

18)

(0.0

27)

(0.0

24)

(0.0

24)

(0.0

19)

(0.0

79)

(0.0

79)

(0.1

82)

(0.2

21)

CB

D 5

0.0

25*

0.01

80.

020

0.02

00.

015

-0.0

12

-0.0

56

0.11

40.

066

(0.0

14)

(0.0

17)

(0.0

16)

(0.0

15)

(0.0

13)

(0.0

64)

(0.0

56)

(0.1

31)

(0.1

55)

CB

D 6

0.01

9-0

.000

-0

.000

-0

.003

0.

005

0.0

60*

0.05

30.

049

0.11

0(0

.015

)(0

.015

)(0

.014

)(0

.014

)(0

.013

)(0

.032

)(0

.035

)(0

.088

)(0

.086

)

Inne

r Bou

ndar

y 1-

6Ye

sYe

sYe

sYe

sYe

sO

uter

Bou

ndar

y 1-

6Ye

sYe

sYe

sYe

sYe

sK

udam

m 1

-6Ye

sYe

sYe

sYe

sB

lock

Cha

ract

eris

tics

Yes

Yes

Yes

Dis

trict

Fix

ed E

ffect

sYe

sYe

sYe

sYe

sYe

sYe

sYe

sYe

s

Obs

erva

tions

7050

7050

7050

7050

7050

6718

6718

5602

5602

R-s

quar

ed0.

080.

320.

340.

350.

430.

040.

070.

030.

06

Not

e: T

his t

able

repo

rts a

robu

stne

s tes

t for

Tab

le 2

in th

e pa

per u

sing

clu

ster

ed st

anda

rd e

rror

s. Q

den

otes

the

pric

e of

floo

r spa

ce. E

mpR

den

otes

em

ploy

men

t by

resi

denc

e.

EmpW

den

otes

em

ploy

men

t by

wor

kpla

ce. C

BD

1-C

BD

6 ar

e si

x 50

0m d

ista

nce

grid

cel

ls fo

r dis

tanc

e fr

om th

e pr

e-w

ar C

BD

. Inn

er B

ound

ary

1-6

are

six

500m

grid

cel

ls fo

r di

stan

ce to

the

Inne

r Bou

ndar

y be

twee

n Ea

st a

nd W

est B

erlin

. Out

er B

ound

ary

1-6

are

six

500m

grid

cel

ls fo

r dis

tanc

e to

the

oute

r bou

ndar

y be

twee

n W

est B

erlin

and

Eas

t G

erm

any.

Kud

amm

1-6

are

six

500m

grid

cel

ls fo

r dis

tanc

e to

Bre

itsch

eid

Plat

z on

the

Kur

fürs

tend

amm

. Blo

ck c

hara

cter

istic

s inc

lude

the

loga

rithm

of d

ista

nce

to sc

hool

s, pa

rks

and

wat

er, t

he la

nd a

rea

of th

e bl

ock,

the

shar

e of

the

bloc

k's b

uilt-

up a

rea

dest

roye

d du

ring

the

Seco

nd W

orld

War

, ind

icat

ors f

or re

side

ntia

l, co

mm

erci

al a

nd in

dust

rial l

and

use,

an

d in

dica

tors

for w

heth

er a

blo

ck in

clud

es a

gov

ernm

ent b

uild

ing

and

urba

n re

gene

ratio

n po

licie

s pos

t-reu

nific

atio

n. R

obus

t Sta

ndar

d Er

rors

in P

aren

thes

es a

djus

ted

for

clus

terin

g by

stat

istic

al a

rea

("G

ebie

te")

. * si

gnifi

cant

at 1

0%; *

* si

gnifi

cant

at 5

%; *

** si

gnifi

cant

at 1

%.

Table A.3: Robustness Test for Baseline Reunication Results (1986-2006), Clustered Standard Errors

85

(3)

(4)

(5)

(7)

(9)

(4)

(5)

(7)

(9)

Δ ln

QΔ

ln Q

Δ ln

QΔ

ln E

mpR

Δ ln

Em

pWΔ

ln Q

Δ ln

QΔ

ln E

mpR

Δ ln

Em

pW

INN

1

0.03

5**

0.

033*

* 0

.030

*0.

031

-0.0

30

KU

1

0.0

85**

*0.

027

-0.2

31

0.15

9(0

.016

)(0

.016

)(0

.016

)(0

.047

)(0

.113

)(0

.024

)(0

.024

)(0

.176

)(0

.203

)IN

N 2

0.01

90.

018

0.01

6-0

.010

0.

006

KU

2 0

.032

*0.

008

-0.1

02

0.29

5**

(0.0

22)

(0.0

22)

(0.0

22)

(0.0

32)

(0.1

18)

(0.0

18)

(0.0

16)

(0.0

68)

(0.1

38)

INN

3-0

.017

*-0

.018

*-0

.017

*0.

004

-0.0

86

KU

30.

017

0.02

10.

014

-0.0

15(0

.010

)(0

.010

)(0

.009

)(0

.029

)(0

.093

)(0

.014

)(0

.013

)(0

.037

)(0

.118

)IN

N 4

-0

.025

***

-0

.026

***

-0

.026

***

0.

075*

*-0

.098

K

U 4

-0.0

17

-0.0

09

0.00

60.

022

(0.0

09)

(0.0

09)

(0.0

08)

(0.0

35)

(0.1

03)

(0.0

12)

(0.0

12)

(0.0

32)

(0.0

97)

INN

5

-0.0

36**

*

-0.0

38**

*

-0.0

42**

*-0

.017

-0

.087

K

U 5

-0

.031

***

'-0.

020*

*0.

007

-0.0

75

(0.0

10)

(0.0

10)

(0.0

08)

(0.0

33)

(0.0

99)

(0.0

11)

(0.0

10)

(0.0

40)

(0.1

37)

INN

6 -

0.01

9**

-0

.024

***

-0

.023

***

-0.0

00

-0.1

50

KU

6-0

.006

0.

006

0.05

2-0

.047

(0

.009

)(0

.009

)(0

.008

)(0

.032

)(0

.092

)(0

.016

)(0

.016

)(0

.045

)(0

.116

)O

UT

1-0

.011

-0

.011

-0

.006

0.

039

0.09

5(0

.015

)(0

.015

)(0

.016

)(0

.030

)(0

.102

)O

UT

2

-0.0

30**

*

-0.0

30**

*

-0.0

26**

*0.

012

0.06

6(0

.006

)(0

.006

)(0

.006

)(0

.027

)(0

.079

)O

UT

3

-0.0

30**

*

-0.0

30**

*

-0.0

25**

*0.

009

0.14

4(0

.006

)(0

.006

)(0

.006

)(0

.032

)(0

.088

)O

UT

4

-0.0

30**

*

-0.0

30**

*

-0.0

21**

*-0

.001

0.

014

(0.0

07)

(0.0

06)

(0.0

07)

(0.0

26)

(0.0

77)

OU

T 5

-0

.030

***

-0

.030

***

-0

.024

***

-0.0

31

0.01

3(0

.006

)(0

.006

)(0

.006

)(0

.026

)(0

.079

)O

UT

6

-0.0

19**

*

-0.0

19**

*

-0.0

16**

*0.

011

-0.0

88

(0.0

07)

(0.0

07)

(0.0

06)

(0.0

37)

(0.0

95)

Tabl

e A4:

Bas

elin

e R

euni

ficat

ion

Res

ults

(198

6-20

06),

Add

ition

al C

oeff

icie

nts,

Con

ley

Stan

dard

Err

ors

Not

e: T

his t

able

repo

rts th

e co

effic

ient

s and

stan

dard

err

ors o

n th

e ad

ditio

nal d

ista

nce

grid

cel

ls in

Tab

le 2

in th

e pa

per.

Q d

enot

es th

e pr

ice

of fl

oor s

pace

. Em

pR d

enot

es

empl

oym

ent b

y re

side

nce.

Em

pW d

enot

es e

mpl

oym

ent b

y w

orkp

lace

. IN

N1-

INN

6 ar

e si

x 50

0m d

ista

nce

grid

cel

ls fo

r dis

tanc

e fr

om th

e in

ner b

ound

ary

betw

een

East

and

Wes

t B

erlin

. OU

T1-O

UT6

are

six

500m

grid

cel

ls fo

r dis

tanc

e to

the

Out

er B

ound

ary

betw

een

Wes

t Ber

lin a

nd E

ast G

erm

any.

KU

1-K

U6

are

six

500m

grid

cel

ls fo

r dis

tanc

e to

B

reits

chei

d Pl

atz

on th

e K

urfü

rste

ndam

m. C

olum

n nu

mbe

rs re

fer t

o th

e co

lum

n nu

mbe

rs in

Tab

le 2

in th

e pa

per.

See

Tabl

e 2

in th

e pa

per f

or fu

rther

det

ails

. Het

eros

ceda

stic

ity a

nd

Aut

ocor

rela

tion

Con

sist

ent (

HA

C) s

tand

ard

erro

rs in

par

enth

eses

(Con

ley

1999

). *

sign

ifica

nt a

t 10%

; **

sign

ifica

nt a

t 5%

; ***

sign

ifica

nt a

t 1%

.

Table A.4: Other Coecients from Baseline Reunication Results (1986-2006), Conley Standard Errors

86

(1) (2) (3) (4) (5)Δ ln Q Δ ln Q Δ ln Q Δ ln Q Δ ln Q

CBD 1 -0.718*** -0.506*** -0.493*** -0.475*** -0.489***(0.039) (0.046) (0.047) (0.047) (0.050)

CBD 2 -0.605*** -0.393*** -0.381*** -0.354*** -0.368***(0.027) (0.034) (0.035) (0.033) (0.035)

CBD 3 -0.485*** -0.274*** -0.264*** -0.235*** -0.246***(0.024) (0.031) (0.030) (0.027) (0.028)

CBD 4 -0.410*** -0.209*** -0.195*** -0.173*** -0.171***(0.014) (0.025) (0.025) (0.022) (0.021)

CBD 5 -0.328*** -0.141*** -0.126*** -0.104*** -0.101***(0.014) (0.018) (0.018) (0.019) (0.018)

CBD 6 -0.249*** -0.113*** -0.090*** -0.074*** -0.070***(0.016) (0.015) (0.013) (0.013) (0.013)

Inner Boundary 1-6 Yes Yes YesOuter Boundary 1-6 Yes Yes YesKudamm 1-6 Yes YesBlock Characteristics YesDistrict Fixed Effects Yes Yes Yes Yes

Observations 6260 6260 6260 6260 6260R-squared 0.34 0.58 0.67 0.69 0.70

Note: Q denotes price of floor space. CBD1-CBD6 are six 500m distance grid cells for distance from the pre-war CBD. Inner Boundary 1-6 are six 500m grid cells for distance to the Inner Boundary between East and West Berlin. Outer Boundary 1-6 are six 500m grid cells for distance to the outer boundary between West Berlin and East Germany. Kudamm 1-6 are six 500m grid cells for distance to Breitscheid Platz on the Kurfürstendamm. Block characteristics include the logarithm of distance to schools, parks and water, the land area of the block, the share of the block's built-up area destroyed during the Second World War, indicators for residential, commercial and industrial land use, and indicators for whether a block includes a government building and urban regeneration policies post-reunification. Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors in parentheses (Conley 1999). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A.5: Early Division Period (1936-66), Conley Standard Errors

87

(1) (2) (3) (4) (5)Δ ln Q Δ ln Q Δ ln Q Δ ln Q Δ ln Q

CBD 1 -0.718*** -0.506*** -0.493*** -0.475*** -0.489***(0.051) (0.065) (0.069) (0.068) (0.074)

CBD 2 -0.605*** -0.393*** -0.381*** -0.354*** -0.368***(0.029) (0.047) (0.051) (0.046) (0.053)

CBD 3 -0.485*** -0.274*** -0.264*** -0.235*** -0.246***(0.040) (0.051) (0.052) (0.047) (0.051)

CBD 4 -0.410*** -0.209*** -0.195*** -0.173*** -0.171***(0.022) (0.033) (0.035) (0.032) (0.030)

CBD 5 -0.328*** -0.141*** -0.126*** -0.104*** -0.101***(0.022) (0.021) (0.023) (0.024) (0.022)

CBD 6 -0.249*** -0.113*** -0.090*** -0.074*** -0.070***(0.030) (0.021) (0.020) (0.018) (0.018)

Inner Boundary 1-6 Yes Yes YesOuter Boundary 1-6 Yes Yes YesKudamm 1-6 Yes YesBlock Characteristics YesDistrict Fixed Effects Yes Yes Yes Yes

Observations 6260 6260 6260 6260 6260R-squared 0.34 0.58 0.67 0.69 0.70

Note: This table reports a robustness test for Table A5 in this web appendix using clustered standard errors. Q denotes price of floor space. CBD1-CBD6 are six 500m distance grid cells for distance from the pre-war CBD. Inner Boundary 1-6 are six 500m grid cells for distance to the Inner Boundary between East and West Berlin. Outer Boundary 1-6 are six 500m grid cells for distance to the outer boundary between West Berlin and East Germany. Kudamm 1-6 are six 500m grid cells for distance to Breitscheid Platz on the Kurfürstendamm. Block characteristics include the logarithm of distance to schools, parks and water, the land area of the block, the share of the block's built-up area destroyed during the Second World War, indicators for residential, commercial and industrial land use, and indicators for whether a block includes a government building and urban regeneration policies post-reunification. Robust Standard Errors in Parentheses adjusted for clustering by statistical area ("Gebiete"). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A.6: Robustness Test for Early Division Period (1936-66), Clustered Standard Errors

88

(1) (2) (3) (4) (5)Δ ln Q Δ ln Q Δ ln Q Δ ln Q Δ ln Q

CBD 1 -0.083** -0.061** -0.030 -0.028 -0.077**(0.035) (0.031) (0.032) (0.032) (0.036)

CBD 2 -0.050** -0.029 -0.012 -0.007 -0.032(0.022) (0.023) (0.023) (0.023) (0.025)

CBD 3 -0.058*** -0.032 -0.030 -0.023 -0.001(0.020) (0.023) (0.023) (0.023) (0.018)

CBD 4 -0.027* 0.002 0.002 0.007 -0.005(0.015) (0.019) (0.019) (0.020) (0.016)

CBD 5 -0.026*** 0.002 0.004 0.006 0.001(0.009) (0.013) (0.014) (0.014) (0.011)

CBD 6 -0.042*** -0.013 -0.004 -0.003 -0.020**(0.010) (0.012) (0.012) (0.012) (0.010)

Inner Boundary 1-6 Yes Yes YesOuter Boundary 1-6 Yes Yes YesKudamm 1-6 Yes YesBlock Characteristics YesDistrict Fixed Effects Yes Yes Yes Yes

Observations 6260 6260 6260 6260 6260R-squared 0.01 0.10 0.17 0.17 0.45

Table A7: Timing of Division Impact (Late Period, 1966-1986)

Note: Q denotes price of floor space. CBD1-CBD6 are six 500m distance grid cells for distance from the pre-war CBD. Inner Boundary 1-6 are six 500m grid cells for distance to the Inner Boundary between East and West Berlin. Outer Boundary 1-6 are six 500m grid cells for distance to the outer boundary between West Berlin and East Germany. Kudamm 1-6 are six 500m grid cells for distance to Breitscheid Platz on the Kurfürstendamm. Block characteristics include the logarithm of distance to schools, parks and water, the land area of the block, the share of the block's built-up area destroyed during the Second World War, indicators for residential, commercial and industrial land use, and indicators for whether a block includes a government building and urban regeneration policies post-reunification. Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors in parentheses (Conley 1999). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A.7: Late Division Period (1966-86), Conley Standard Errors

89

(1) (2) (3) (4) (5)Δ ln Q Δ ln Q Δ ln Q Δ ln Q Δ ln Q

CBD 1 -0.083 -0.061 -0.030 -0.028 -0.077(0.057) (0.051) (0.052) (0.052) (0.051)

CBD 2 -0.050 -0.029 -0.012 -0.007 -0.032(0.034) (0.036) (0.036) (0.034) (0.032)

CBD 3 -0.058*** -0.032 -0.030 -0.023 -0.001(0.019) (0.031) (0.034) (0.033) (0.023)

CBD 4 -0.027 0.002 0.002 0.007 -0.005(0.020) (0.020) (0.024) (0.022) (0.017)

CBD 5 -0.026* 0.002 0.004 0.006 0.001(0.015) (0.020) (0.022) (0.021) (0.013)

CBD 6 -0.042*** -0.013 -0.004 -0.003 -0.020*(0.014) (0.017) (0.016) (0.016) (0.011)

Inner Boundary 1-6 Yes Yes YesOuter Boundary 1-6 Yes Yes YesKudamm 1-6 Yes YesBlock Characteristics YesDistrict Fixed Effects Yes Yes Yes Yes

Observations 6260 6260 6260 6260 6260R-squared 0.01 0.10 0.17 0.17 0.45

Table A8: Timing of Division Impact (Late Period, 1966-1986, Clustered Standard Errors)

Note: This table reports a robustness test for Table A7 in this web appendix using clustered standard errors. Q denotes price of floor space. CBD1-CBD6 are six 500m distance grid cells for distance from the pre-war CBD. Inner Boundary 1-6 are six 500m grid cells for distance to the Inner Boundary between East and West Berlin. Outer Boundary 1-6 are six 500m grid cells for distance to the outer boundary between West Berlin and East Germany. Kudamm 1-6 are six 500m grid cells for distance to Breitscheid Platz on the Kurfürstendamm. Block characteristics include the logarithm of distance to schools, parks and water, the land area of the block, the share of the block's built-up area destroyed during the Second World War, indicators for residential, commercial and industrial land use, and indicators for whether a block includes a government building and urban regeneration policies post-reunification. Robust Standard Errors in Parentheses adjusted for clustering by statistical area ("Gebiete"). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A.8: Robustness Test for Late Division Period (1966-86), Clustered Standard Errors

90

(1) (2) (3) (4) (5) (6)Δ ln Q Δ ln Q Δ ln Q Δ ln Q Δ ln Q Δ ln Q

1936-86 1936-86 1936-86 1986-2006 1986-2006 1986-2006

CBD 1 -0.736*** -0.533*** -0.548*** 0.381*** 0.402*** 0.280***(0.059) (0.062) (0.071) (0.101) (0.088) (0.087)

CBD 2 -0.627*** -0.407*** -0.395*** 0.282** 0.287*** 0.190**(0.046) (0.047) (0.051) (0.112) (0.096) (0.087)

CBD 3 -0.515*** -0.291*** -0.241*** 0.115*** 0.118*** 0.063**(0.038) (0.039) (0.034) (0.039) (0.033) (0.028)

CBD 4 -0.403*** -0.192*** -0.169*** 0.024* 0.029 0.016(0.021) (0.031) (0.025) (0.014) (0.023) (0.020)

CBD 5 -0.332*** -0.131*** -0.098*** 0.019* 0.016 0.015(0.018) (0.024) (0.020) (0.010) (0.015) (0.013)

CBD 6 -0.276*** -0.120*** -0.088*** 0.015* -0.001 0.005(0.016) (0.019) (0.016) (0.009) (0.012) (0.011)

U/S-Bahn -0.143*** -0.077*** -0.049*** 0.037*** 0.012** 0.005(0.012) (0.010) (0.008) (0.007) (0.006) (0.005)

Inner Boundary 1-6 Yes YesOuter Boundary 1-6 Yes YesKudamm 1-6 Yes YesBlock Characteristics Yes YesDistrict Fixed Effects Yes Yes Yes Yes

Observations 6260 6260 6260 7050 7050 7050R-squared 0.30 0.52 0.71 0.08 0.32 0.43

Table A9: Transport Access Results (1936-1986 and 1986-2006, Conley Standard Errors)

Note: Q denotes price of floor space. CBD1-CBD6 are six 500m distance grid cells for distance from the pre-war CBD. U/S-Bahn is an indicator variable that is one if a block lies within 250 meters of a U-bahn or S-bahn station and zero otherwise. Inner Boundary 1-6 are six 500m grid cells for distance to the Inner Boundary between East and West Berlin. Outer Boundary 1-6 are six 500m grid cells for distance to the outer boundary between West Berlin and East Germany. Kudamm 1-6 are six 500m grid cells for distance to Breitscheid Platz on the Kurfürstendamm. Block characteristics include the logarithm of distance to schools, parks and water, the land area of the block, the share of the block's built-up area destroyed during the Second World War, indicators for residential, commercial and industrial land use, and indicators for whether a block includes a government building and urban regeneration policies post-reunification. Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors in parentheses (Conley 1999). * significant at 10%; ** significant at 5%; *** significant at 1%.statistical area ("Gebiete"). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A.9: Transport Access Results for Division and Reunication (1936-86 and 1986-2006), Conley Stan-dard Errors

91

(1) (2) (3) (4) (5) (6)Δ ln Q Δ ln Q Δ ln Q Δ ln Q Δ ln Q Δ ln Q

1936-86 1936-86 1936-86 1986-2006 1986-2006 1986-2006

CBD 1 -0.736*** -0.533*** -0.548*** 0.381** 0.402*** 0.280**(0.086) (0.094) (0.108) (0.149) (0.125) (0.120)

CBD 2 -0.627*** -0.407*** -0.395*** 0.282* 0.287** 0.190(0.066) (0.069) (0.073) (0.167) (0.136) (0.125)

CBD 3 -0.515*** -0.291*** -0.241*** 0.115** 0.118** 0.063*(0.060) (0.059) (0.064) (0.053) (0.047) (0.033)

CBD 4 -0.403*** -0.192*** -0.169*** 0.024 0.029 0.016(0.031) (0.039) (0.035) (0.019) (0.027) (0.019)

CBD 5 -0.332*** -0.131*** -0.098*** 0.019 0.016 0.015(0.027) (0.029) (0.024) (0.014) (0.017) (0.013)

CBD 6 -0.276*** -0.120*** -0.088*** 0.015 -0.001 0.005(0.031) (0.028) (0.023) (0.013) (0.015) (0.013)

U/S-Bahn -0.143*** -0.077*** -0.049*** 0.037*** 0.012** 0.005(0.019) (0.014) (0.010) (0.008) (0.005) (0.005)

Inner Boundry 1-6 Yes YesOuter Boundary 1-6 Yes YesKudamm 1-6 Yes YesBlock Characteristics Yes YesDistrict Fixed Effects Yes Yes Yes Yes

Observations 6260 6260 6260 7050 7050 7050R-squared 0.30 0.52 0.71 0.08 0.32 0.43

Note: This table reports a robustness test for Table A9 in this web appendix using clustered standard errors. Q denotes price of floor space. CBD1-CBD6 are six 500m distance grid cells for distance from the pre-war CBD. U/S-Bahn is an indicator variable that is one if a block lies within 250 meters of a U-bahn or S-bahn station and zero otherwise. Inner Boundary 1-6 are six 500m grid cells for distance to the Inner Boundary between East and West Berlin. Outer Boundary 1-6 are six 500m grid cells for distance to the outer boundary between West Berlin and East Germany. Kudamm 1-6 are six 500m grid cells for distance to Breitscheid Platz on the Kurfürstendamm. Block characteristics include the logarithm of distance to schools, parks and water, the land area of the block, the share of the block's built-up area destroyed during the Second World War, indicators for residential, commercial and industrial land use, and indicators for whether a block includes a government building and urban regeneration policies post-reunification. Standard errors in parentheses are heteroscedasticity robust and clustered on statistical area (Gebiete). * significant at 10%; ** significant at 5%; *** significant at 1%.statistical area ("Gebiete"). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A.10: Robustness Test for Transport Access Results for Division and Reunication (1936-86 and 1986-2006), Clustered Standard Errors

92

(1) (2) (3) (4) (5) (6)Δ ln A Δ ln B Δ ln A Δ ln B Δ ln QC Δ ln QC

1936-86 1936-86 1986-2006 1986-2006 1936-1986 1986-2006

CBD 1 -0.207*** -0.347*** 0.261** 0.203*** -0.408*** -0.010 (0.065) (0.089) (0.109) (0.060) (0.063) (0.017)

CBD 2 -0.260*** -0.242*** 0.144** 0.109 -0.348*** 0.079(0.038) (0.064) (0.071) (0.071) (0.042) (0.052)

CBD 3 -0.138*** -0.262*** 0.077*** 0.059* -0.353*** 0.036(0.030) (0.037) (0.024) (0.032) (0.046) (0.047)

CBD 4 -0.131*** -0.154*** 0.057*** 0.010 -0.378*** 0.093***(0.015) (0.031) (0.016) (0.010) (0.045) (0.035)

CBD 5 -0.095*** -0.126*** 0.028** -0.014 -0.380*** 0.115**(0.016) (0.020) (0.013) (0.010) (0.049) (0.054)

CBD 6 -0.061*** -0.117*** 0.023** 0.001 -0.354*** 0.066*(0.021) (0.026) (0.010) (0.006) (0.044) (0.035)

Counterfactuals Yes YesAgglomeration Effects No No

Observations 2844 5978 5602 6718 6260 7050R-squared 0.09 0.06 0.02 0.03 0.07 0.03

Table A11: Floor Prices, Productivity and Amenities (Clustered Standard Errors)

Note: This table reports a robustness test for Table 4 in the paper using clustered standard errors. Columns (1)-(4) based on calibrating the model for ν=εκ=0.07 and ε=6.83 from the gravity equation estimation. Columns (5)-(6) report counterfactuals for these parameter values. A denotes adjusted overall productivity. B denotes adjusted overall amenities. QC denotes counterfactual floor prices (simulating the effect of division on West Berlin). Column (5) simulates division holding A and B constant at their 1936 values. Column (6) simulates reunification holding A and B for West Berlin constant at their 1986 values and using 1936 values of A and B for East Berlin. CBD1-CBD6 are six 500m distance grid cells for distance from the pre-war CBD. Robust Standard Errors in Parentheses adjusted for clustering by statistical area ("Gebiete"). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A.11: Robustness Test for Productivity, Amenities and Counterfactual Floor Prices, Clustered StandardErrors

93

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Δ ln

Aλ Δ

ln U

psilo

nΔ

ln a

Δ ln

Bη

Δ ln

Om

ega

Δ ln

bΔ

ln A

λ Δ

ln U

psilo

nΔ

ln a

Δ ln

Bη

Δ ln

Om

ega

Δ ln

b19

36-8

619

36-8

619

36-8

619

36-8

619

36-8

619

36-1

986

1986

-200

619

86-2

006

1986

-200

619

86-2

006

1986

-200

619

86-2

006

CB

D 1

-0.2

09**

*-0

.209

***

0.00

0-0

.309

***

-0.3

16**

*0.

007

0.25

2***

0.16

3***

0.08

9*0.

189*

**0.

147*

**0.

042*

(0.0

47)

(0.0

12)

(0.0

40)

(0.0

70)

(0.0

56)

(0.0

30)

(0.0

71)

(0.0

20)

(0.0

53)

(0.0

53)

(0.0

35)

(0.0

25)

CB

D 2

-0.2

69**

*-0

.161

***

-0.1

08**

*-0

.209

***

-0.2

06**

*-0

.004

0.13

7**

0.12

8***

0.00

90.

099*

0.08

8***

0.01

1(0

.032

)(0

.010

)(0

.026

)(0

.056

)(0

.026

)(0

.040

)(0

.056

)(0

.020

)(0

.042

)(0

.058

)(0

.026

)(0

.034

)C

BD

3-0

.146

***

-0.1

19**

*-0

.028

-0.2

38**

*-0

.189

***

-0.0

49*

0.07

3***

0.07

8***

-0.0

050.

052*

*0.

059*

**-0

.007

(0.0

22)

(0.0

09)

(0.0

18)

(0.0

39)

(0.0

14)

(0.0

29)

(0.0

24)

(0.0

07)

(0.0

23)

(0.0

26)

(0.0

20)

(0.0

23)

CB

D 4

-0.1

40**

*-0

.108

***

-0.0

32*

-0.1

32**

*-0

.154

***

0.02

10.

055*

**0.

057*

**-0

.002

0.00

40.

013

-0.0

09(0

.017

)(0

.006

)(0

.017

)(0

.025

)(0

.013

)(0

.019

)(0

.015

)(0

.003

)(0

.015

)(0

.008

)(0

.008

)(0

.008

)C

BD

5-0

.102

***

-0.0

87**

*-0

.015

-0.1

07**

*-0

.164

***

0.05

6***

0.02

5*0.

046*

**-0

.021

-0.0

20**

*0.

014*

**-0

.034

***

(0.0

14)

(0.0

08)

(0.0

12)

(0.0

14)

(0.0

11)

(0.0

15)

(0.0

14)

(0.0

04)

(0.0

14)

(0.0

08)

(0.0

05)

(0.0

09)

CB

D 6

-0.0

66**

*-0

.065

***

-0.0

00-0

.106

***

-0.1

51**

*0.

045*

**0.

021*

*0.

041*

**-0

.021

*-0

.004

0.00

9**

-0.0

12**

(0.0

15)

(0.0

07)

(0.0

13)

(0.0

16)

(0.0

10)

(0.0

12)

(0.0

10)

(0.0

04)

(0.0

11)

(0.0

06)

(0.0

04)

(0.0

06)

Obs

erva

tions

2844

2844

2844

5978

5978

5978

5602

5602

5602

6718

6718

6718

R-s

quar

ed0.

080.

360.

010.

030.

090.

010.

020.

200.

000.

020.

050.

01

Tabl

e A12

: Fun

dam

enta

ls a

nd E

xter

nalit

ies (

Con

ley

Stan

dard

Err

ors)

Not

e: T

his t

able

is b

ased

on

the

para

met

er e

stim

ates

from

poo

ling

divi

sion

and

reun

ifica

tion.

A d

enot

es a

djus

ted

over

all p

rodu

ctiv

ity. U

psilo

n de

note

s pro

duct

ion

exte

rnal

ities

. a d

enot

es a

djus

ted

prod

uctio

n fu

ndam

enta

ls. B

den

otes

ad

just

ed o

vera

ll am

eniti

es. O

meg

a de

note

s res

iden

tial e

xter

nalit

ies.

b de

note

s adj

uste

d pr

oduc

tion

fund

amen

tals

. CB

D1-

CB

D6

are

six

500m

dis

tanc

e gr

id c

ells

for d

ista

nce

from

the

pre-

war

CB

D. H

eter

osce

dast

icity

and

Aut

ocor

rela

tion

Con

sist

ent (

HA

C) s

tand

ard

erro

rs in

par

enth

eses

(Con

ley

1999

). *

sign

ifica

nt a

t 10%

; **

sign

ifica

nt a

t 5%

; ***

sign

ifica

nt a

t 1%

.

Table A.12: Fundamentals and Externalities (Parameter Estimates Pooling Division and Reunication, Con-ley Standard Errors)

94

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Δ ln

Aλ Δ

ln U

psilo

nΔ

ln a

Δ ln

Bη

Δ ln

Om

ega

Δ ln

bΔ

ln A

λ Δ

ln U

psilo

nΔ

ln a

Δ ln

Bη

Δ ln

Om

ega

Δ ln

b19

36-8

619

36-8

619

36-8

619

36-8

619

36-8

619

36-1

986

1986

-200

619

86-2

006

1986

-200

619

86-2

006

1986

-200

619

86-2

006

CB

D 1

-0.2

09**

*-0

.209

***

0.00

0-0

.309

***

-0.3

16**

*0.

007

0.25

2**

0.16

3***

0.08

90.

189*

**0.

147*

**0.

042*

*(0

.062

)(0

.018

)(0

.047

)(0

.090

)(0

.068

)(0

.025

)(0

.106

)(0

.029

)(0

.078

)(0

.059

)(0

.042

)(0

.017

)C

BD

2-0

.269

***

-0.1

61**

*-0

.108

***

-0.2

09**

*-0

.206

***

-0.0

040.

137*

0.12

8***

0.00

90.

099

0.08

8***

0.01

1(0

.039

)(0

.014

)(0

.025

)(0

.068

)(0

.039

)(0

.046

)(0

.070

)(0

.031

)(0

.044

)(0

.070

)(0

.029

)(0

.041

)C

BD

3-0

.146

***

-0.1

19**

*-0

.028

-0.2

38**

*-0

.189

***

-0.0

490.

073*

**0.

078*

**-0

.005

0.05

20.

059*

*-0

.007

(0.0

32)

(0.0

16)

(0.0

21)

(0.0

44)

(0.0

15)

(0.0

35)

(0.0

24)

(0.0

08)

(0.0

21)

(0.0

32)

(0.0

23)

(0.0

25)

CB

D 4

-0.1

40**

*-0

.108

***

-0.0

32*

-0.1

32**

*-0

.154

***

0.02

10.

055*

**0.

057*

**-0

.002

0.00

40.

013

-0.0

09(0

.017

)(0

.009

)(0

.016

)(0

.038

)(0

.019

)(0

.026

)(0

.017

)(0

.005

)(0

.017

)(0

.011

)(0

.009

)(0

.011

)C

BD

5-0

.102

***

-0.0

87**

*-0

.015

-0.1

07**

*-0

.164

***

0.05

6**

0.02

5*0.

046*

**-0

.021

-0.0

20*

0.01

4*-0

.034

***

(0.0

18)

(0.0

12)

(0.0

14)

(0.0

27)

(0.0

19)

(0.0

23)

(0.0

13)

(0.0

06)

(0.0

14)

(0.0

12)

(0.0

07)

(0.0

12)

CB

D 6

-0.0

66**

*-0

.065

***

-0.0

00-0

.106

***

-0.1

51**

*0.

045*

*0.

021*

*0.

041*

**-0

.021

-0.0

040.

009*

-0.0

12(0

.023

)(0

.009

)(0

.021

)(0

.032

)(0

.020

)(0

.021

)(0

.010

)(0

.006

)(0

.012

)(0

.007

)(0

.005

)(0

.008

)

Obs

erva

tions

2844

2844

2844

5978

5978

5978

5602

5602

5602

6718

6718

6718

R-s

quar

ed0.

080.

360.

010.

030.

090.

010.

020.

200.

000.

020.

050.

01

Tabl

e A13

: Fun

dam

enta

ls a

nd E

xter

nalit

ies (

Clu

ster

ed S

tand

ard

Err

ors)

Not

e: T

his t

able

is b

ased

on

the

para

met

er e

stim

ates

from

poo

ling

divi

sion

and

reun

ifica

tion.

A d

enot

es a

djus

ted

over

all p

rodu

ctiv

ity. U

psilo

n de

note

s pro

duct

ion

exte

rnal

ities

. a d

enot

es a

djus

ted

prod

uctio

n fu

ndam

enta

ls. B

den

otes

ad

just

ed o

vera

ll am

eniti

es. O

meg

a de

note

s res

iden

tial e

xter

nalit

ies.

b de

note

s adj

uste

d pr

oduc

tion

fund

amen

tals

. CB

D1-

CB

D6

are

six

500m

dis

tanc

e gr

id c

ells

for d

ista

nce

from

the

pre-

war

CB

D. R

obus

t Sta

ndar

d Er

rors

in P

aren

thes

es

adju

sted

for c

lust

erin

g by

stat

istic

al a

rea

("G

ebie

te")

. * si

gnifi

cant

at 1

0%; *

* si

gnifi

cant

at 5

%; *

** si

gnifi

cant

at 1

%.

Table A.13: Robustness Test for Fundamentals and Externalities (Parameter Estimates Pooling Division andReunication, Clustered Standard Errors)

95

(1) (2) (3)Division

Efficient GMMReunification

Efficient GMMDivision and Reunification

Efficient GMM

Productivity Elasticity (λ) 0.0725*** 0.0544*** 0.0665***(0.0047) (0.0087) (0.0047)

Productivity Decay (δ) 0.3621*** 0.7580*** 0.3652***(0.1250) (0.2688) (0.0956)

Residential Elasticity (η) 0.1472*** 0.1152*** 0.1469***(0.0064) (0.0153) (0.0074)

Residential Decay (ρ) 0.8425*** 0.5281*** 0.6282***(0.2233) (0.1981) (0.1730)

Table A14: Generalized Method of Moments (GMM) Robustness

Note: Generalized Method of Moments (GMM) estimates. Robustness to using assumed values of ν = εκ = 0.07 and ε = 6.83 and estimating the agglomeration parameters λ, δ, ε, ρ. Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors in parentheses (Conley 1999). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A.14: Robustness Test for Generalized Method of Moments (GMM) Estimation

96

(1) (2)

ln Model Ratio Floor Space to Land Area

2006

ln Model Ratio Floor Space to Land Area

2006

ln Data Ratio Floor Space to Land Area 2006 0.959*** 0.959***(0.018) (0.030)

Standard Errors Conley ClusteredObservations 7050 7050R-squared 0.36 0.36

Note: The table is based on the parameter estimates pooling division and reunification from Table 5 of the paper. The dependent variable is the logarithm of the ratio of floor space to land area in the model (L/K) for 2006. The independent variable is the logarithm of the ratio of floor space to land area (GFZ) in the data for 2006. Column (1) reports Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors following Conley (1999). Column (2) reports standard errors clustered by statistical area ("Gebiet"). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A15 : Ratio of Floor Space to Ground Area Overidentification Check

Table A.15: Ratio of Floor Space to Land Area Overidentication Check

97

(1) (2) (3) (4)ln Adjusted Production

Fundamental 2006

ln Adjusted Residential

Fundamental 2006

ln Adjusted Production

Fundamental 2006

ln Adjusted Residential

Fundamental 2006

Green Areas 0.007*** 0.020*** 0.007*** 0.020***(0.001) (0.001) (0.001) (0.001)

Water Areas 0.047*** 0.032*** 0.047*** 0.032**(0.007) (0.009) (0.010) (0.015)

War Destruction -0.031* -0.187*** -0.031 -0.187***(0.017) (0.021) (0.024) (0.037)

Listed Buildings 0.057*** 0.030*** 0.057*** 0.030***(0.003) (0.004) (0.005) (0.005)

Noise -0.008 -0.314*** -0.008 -0.314***(0.021) (0.025) (0.037) (0.046)

Standard Errors Conley Conley Clustered ClusteredR-squared 0.134 0.282 0.134 0.282Observations 9437 11863 9437 11863

Note: This table is based on the parameter estimates pooling division and reunification from Table 5 in the paper. The dependent variable in Columns (1) and (3) is the log adjusted production fundamental in the model (a) for 2006. The dependent variable in Columns (2) and (4) is the log adjusted residential fundamental in the model (b) in 2006. The independent variable is the log ratio of floor space to geographical land area (GFZ) in the data for 2006. Green Areas are the logarithm of one plus the square meters of green areas in a block; Water Areas is a dummy which is one if the block is adjacent to a lake, river or canal; War Destruction is the share of the block's built-up area that was destroyed during the Second World War; Listed Buildings is the logarithm of one plus the number of listed buildings in a block; Noise is the logarithm of the average noise level in decibel in a block; Columns (1) and (2) report Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors following Conley (1999). Columns (3) and (4) report standard errors clustered by statistical area ("Gebiet"). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A16: Production and Residential Fundamentals Overidentification Check

Table A.16: Adjusted Production and Residential Fundamentals Overidentication Check

98

(1) (2) (3) (4) (5) (6) (7)Δ ln QC Δ ln QC Δ ln QC Δ ln QC Δ ln QC Δ ln QC Δ ln QC1936-86 1936-86 1936-86 1936-1986 1986-2006 1986-1936 1986-2006

CBD 1 -0.836*** -0.613*** -0.467*** -0.821*** 0.363*** 1.160*** 0.392***(0.065) (0.033) (0.085) (0.072) (0.058) (0.063) (0.060)

CBD 2 -0.560*** -0.397*** -0.364*** -0.624*** 0.239*** 0.779*** 0.244***(0.047) (0.027) (0.039) (0.045) (0.043) (0.029) (0.042)

CBD 3 -0.455*** -0.312*** -0.336*** -0.530*** 0.163*** 0.594*** 0.179***(0.060) (0.044) (0.056) (0.064) (0.042) (0.049) (0.038)

CBD 4 -0.423*** -0.284*** -0.340*** -0.517*** 0.140*** 0.445*** 0.143***(0.046) (0.030) (0.043) (0.051) (0.030) (0.052) (0.029)

CBD 5 -0.418*** -0.265*** -0.351*** -0.512*** 0.177*** 0.403*** 0.180***(0.056) (0.039) (0.050) (0.069) (0.052) (0.051) (0.052)

CBD 6 -0.349*** -0.222*** -0.304*** -0.430*** 0.100*** 0.334*** 0.103***(0.048) (0.031) (0.045) (0.056) (0.037) (0.056) (0.037)0.160*** -0.228***(0.022)

Counterfactuals Yes Yes Yes Yes Yes Yes YesAgglomeration Effects Yes Yes Yes Yes Yes Yes Yes

Observations 6260 6260 6260 6260 7050 6260 7050R-squared 0.11 0.13 0.07 0.13 0.12 0.24 0.13

Note: Columns (1)-(6) are based on the parameter estimates pooling division and reunification from Table 5 in the paper. Column (7) is based on the parameter estimates for division from Table 5 in the paper. QC denotes counterfactual floor prices. Column (1) simulates division using our estimates of production and residential externalities and 1936 fundamentals. Column (2) simulates division using our estimates of production externalities and 1936 fundamentals but setting residential externalities to zero. Column (3) simulates division using our estimates of residential externalities and 1936 fundamentals but setting production externalities to zero. Column (4) simulates division using our estimates of production and residential externalities and 1936 fundamentals but halving their rates of spatial decay with travel time. Column (5) simulates reunification using our estimates of production and residential externalities, 1986 fundamentals for West Berlin, and 2006 fundamentals for East Berlin. Column (6) simulates reunification using our estimates of production and residential externalities, 1986 fundamentals for West Berlin and 1936 fundamentals for East Berlin. Column (7) simulates reunification using our estimates of production and residential externalities, 1986 fundamentals for West Berlin, and 2006 fundamentals for East Berlin (using division rather than pooled parameter estimates). CBD1-CBD6 are six 500m distance grid cells for distance from the pre-war CBD. Robust Standard Errors in Parentheses adjusted for clustering by statistical area ("Gebiete"). * significant at 10%; ** significant at 5%; *** significant at 1%.

Table A17: Counterfactuals (Clustered Standard Errors)

Table A.17: Robustness Test for Counterfactuals, Clustered Standard Errors

99

RowTransport Technology

CounterfactualUnweighted Actual Travel Time (mins)

1. Mean 50.882. Standard Deviation 12.52

Unweighted Counterfactual Travel Time (mins)3. Mean 69.654. Standard Deviation 26.19

Weighted Actual Travel Time (mins)5. Mean (Actual Commuting Weights) 32.03

Weighted Counterfactual Travel Time (mins)6. Mean (Actual Commuting Weights) 37.81

Total City Employment7. Counterfactual/Actual 86.46%

Total City Output8. Counterfactual/Actual 87.55%

Log Change in Block Floor Prices9. Mean -20.04%10. Mean Above Median Treatment Block -29.21%11. Mean Below Median Treatment Block -10.87%

Weighted Counterfactual Travel Time (mins)12. Mean (Counterfactual Commuting Weights) 29.52

Variable

Note: Counterfactual using travel time measures based solely on the public transport network in 2006. Unweighted mean and standard deviation travel times across all possible bilateral connections with positive values of either workplace or residence employment. Weighted mean travel times weight these bilateral travel times by commuting probabilities in either the actual or the counterfactual equilibrium. Above median treatment blocks are those with an above median increase in average unweighted travel times across bilateral connections with positive values of either workplace or residence employment.

Table A.18: Transport Technology Counterfactual

100

Coefficient Standard Error

Year: 2000 -0.073*** (0.020)Year: 2001 -0.105*** (0.021)Year: 2002 -0.142*** (0.020)Year: 2003 -0.176*** (0.019)Year: 2004 -0.193*** (0.020)Year: 2005 -0.124*** (0.017)Year: 2007 0.082*** (0.017)Year: 2008 -0.004 (0.017)Year: 2009 -0.014 (0.019)Year: 2010 0.065*** (0.018)Year: 2011 0.203*** (0.018)Year: 2012 0.279*** (0.023)Age cohort: 5 to 15 years -0.297*** (0.031)Age cohort: 15 to 25 years -0.569*** (0.035)Age cohort: 25 to 35 years -0.783*** (0.035)Age cohort: 35 to 45 years -1.014*** (0.036)Age cohort: 45 to 55 years -1.155*** (0.038)Age cohort: 55 to 65 years -1.021*** (0.039)Age cohort: 65 to 75 years -0.988*** (0.033)Age cohort: 75 to 85 years -1.058*** (0.035)Age cohort: 85 to 95 years -0.967*** (0.039)Age cohort: 95 to 105 years -0.822*** (0.039)Age cohort: 105 to 115 years -0.823*** (0.042)Age cohort: 115 to 125 years -0.859*** (0.048)Age cohort: 125 to 135 years -0.892*** (0.070)Age cohort: 135 to 145 years -0.883*** (0.071)Age cohort: 145 to 155 years -0.854*** (0.135)Age cohort: 155 to 165 years -1.419*** (0.206)Age cohort: 165 to 175 years -1.481*** (0.509)Age cohort: 175 to 185 years -0.430 (0.314)Age cohort: 185 to 195 years -0.607*** (0.115)Age cohort: 195 to 205 years -0.811* (0.462)Age cohort: 205 to 215 years -0.619** (0.306)

Block fixed effectsR-squaredObservations

0.76951,275

Note: This table reports the results of estimating a Case-Shiller type repeated sales specification at the block level using the micro data on property transactions from 2000-2012. Standard errors in parentheses are heteroscedasticity robust and clustered by block. * significant at 10%; ** significant at 5%; *** significant at 1%.

ln(Transaction Price/Lot size)

Yes

Table A.19: Micro Data on Property Transactions

101